Easy math puzzles
Poll
 | 21 votes (45.65%) | ||
| | 14 votes (30.43%) | ||
| | 6 votes (13.04%) | ||
| | 3 votes (6.52%) | ||
| | 12 votes (26.08%) | ||
| | 3 votes (6.52%) | ||
| | 6 votes (13.04%) | ||
| | 5 votes (10.86%) | ||
| | 12 votes (26.08%) | ||
| | 10 votes (21.73%) |
46 members have voted
July 5th, 2023 at 11:40:05 PM
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Quote: ThatDonGuy
I read the problem wrong - I thought it said that that there were was one Ace remaining, rather than one in the already drawn cards (and, as a result, two remaining).
The player wins if there is exactly 1 Ace in the first K-1 cards, and the first card of the remaining 53-K is also an Ace.
There are C(52, K-1) sets of cards for the first K-1, of which 4 C(48, K-2) has exactly one Ace.
If there are three Aces in the last 53-K, the probability that the first is an Ace is 3 / (53-K).
The total probability = 4 C(48, K-2) / C(52, K-1) x 3 / (53 - K) = (K^3 - 104 K^2 + 2755 K - 2652) / 541,450
This is a maximum when K = 18
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Quote: Ace2The probability of winning can be calculated as (k - 1)(52 - k)(52 - k - 1) * 24 / (2 * 52 * 51 * 50 * 49)
Taking the derivative of (k - 1)(52 - k)(52 - k - 1) gives us: 3x^2 - 208x + 2755
Setting that formula to zero and solving for x gives us the maximum value of (104 - 2551^.5) / 3 =~17.83
That’s assuming k is a continuous variable. Since it’s discrete, round to 18
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Correct!!
Very good.
Hmm... I see Ace2 has buzzed in on a 2Ace puzzle. What are the odds?
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Have you tried 22 tonight? I said 22.
July 5th, 2023 at 11:43:18 PM
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I now see that the puzzle says the aim is to have one Ace in the first K cards rather than there's one Ace left in the pack after drawing K cards. Thus my answer would be 52-previous answer.Quote: GialmereSorry guys. Both incorrect.
I'll let this one ride...
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July 6th, 2023 at 3:22:27 PM
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"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 6th, 2023 at 4:17:19 PM
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Each cat is 20, each egg is 1, and each banana is also 1, so the solution is 20 + 2 x 4 = 28.
...which probably means that it's wrong, and that the cats are somehow different
July 6th, 2023 at 4:29:44 PM
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1. What is the one thing in the Constitution (well, now that it's after 1808) that cannot be changed?
The right of every state to have (at least) as many Senators as every other state. Pretty much every time the Republicans manage to stall the Democrats' plans in the Senate, there are calls to make the Senate more proportional, but the founding fathers saw this coming.
The original plan was to have one house of the federal legislature, but the larger states wanted the seats distributed proportional to population, while the smaller states wanted each state to have an equal say; the "Connecticut Compromise" led to the two-house legislature we have.
The bit about 1808 refers to Article V, which says that two parts of Article I could not be amended before 1808; one that prohibits outlawing the importation of slaves, and one that prevents any tax other than a "direct" tax in proportion to the census from being imposed. In fact, both have been amended, by the 13th and 16th Amendments, respectively.
2. What is the one day of the week specified in the Constitution that still applies?
Sunday - in Article I, Section 7, where it says that the President has 10 days to sign or veto a bill, it says, "Sundays excluded." The only other day of the week mentioned in the original - Monday - is in Article I, Section 4: "The Congress shall assemble at least once in every year, and such meeting shall be on the first Monday in December"; however, this was repealed by the 20th Amendment, which moves the mandatory day to January 3.
For a long time, I thought that at least one of "the Supreme Court must meet on the first Monday in October" and "the electors shall cast their votes on the Tuesday after the second Wednesday in December" was in the Constitution, but both are in the United States Code (28 USC 2, and 3 USC 7, respectively).
3. "After the first enumeration required by the first article of the Constitution, there shall be one Representative for every thirty thousand, until the number shall amount to one hundred, after which the proportion shall be so regulated by Congress, that there shall be not less than one hundred Representatives, nor less than one Representative for every forty thousand persons, until the number of Representatives shall amount to two hundred; after which the proportion shall be so regulated by Congress, that there shall not be less than two hundred Representatives, nor more than one Representative for every fifty thousand persons."
What Constitutional significance does this have?
This is the only proposed amendment in the Bill of Rights that has not been ratified. The original Bill had 12 proposed amendments; ten of them became the 1st through 10th Amendments, and another became the 27th Amendment. Since this one says that there must be between 200 and 6600 members of the House of Representatives, there is no rush to get this one ratified...
July 7th, 2023 at 4:02:11 PM
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I constructed the puzzle and made the image above myself, so please don't judge it too harshly.
Give it a try! This one is beer worthy.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 7th, 2023 at 4:31:18 PM
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The equation is the integral over x = -PI/4 to PI/4 of e^(-ix) dx
= e^(-i PI/4) / (-i) - e^(-i (-PI/4)) / (-i)
= -i * (1 / (e^(i PI/4) - 1 / e^(i (-PI/4)))
= -i * (1 / (cos PI/4 + i sin PI/4) - 1 / (cos (-PI/4) + i sin (-PI/4)))
= -i * (1 / (cos PI/4 + i sin PI/4) - 1 / (cos PI/4 - i sin PI/4))
= -i * (1 / (sqrt(2)/2 + i sqrt(2)/2) - 1 / (sqrt(2)/2 - i sqrt(2)/2)
= -i * (-i sqrt(2)) / ((sqrt(2)/2)^2 - (i sqrt(2)/2))
= -i * (-i sqrt(2)) / 1
= -1 * sqrt(2)
= -sqrt(2)
July 7th, 2023 at 4:55:54 PM
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Quote: ThatDonGuyHere is what I get...
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I'll wait a little longer to see what other responses I get. First correct one, which may be yours, gets the beer.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 7th, 2023 at 6:41:28 PM
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July 7th, 2023 at 8:52:39 PM
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Quote: ChesterDog
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I agree! Don, you were close, just the sign was off.
I have enhanced the puzzle a bit to be like the numerous order of operation puzzles I see on Facebook. Just to make sure I'm right, what does the pineapple equal?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 7th, 2023 at 10:18:50 PM
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Quote: WizardQuote: ChesterDog
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I agree! Don, you were close, just the sign was off.
I have enhanced the puzzle a bit to be like the numerous order of operation puzzles I see on Facebook. Just to make sure I'm right, what does the pineapple equal?
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1
apple + apple + apple = 6
3 × apple = 6
apple = 2
1 + apple = lemon
1 + 2 = lemon
3 = lemon
apple + lemon = banana
2 + 3 = banana
5 = banana
banana + banana + banana = orange
5 + 5 + 5 = orange
15 = orange
apple lemon ÷ apple × (apple + apple) - orange = pineapple
23 ÷ 2 × (2 + 2) - 15 = pineapple
23 ÷ 2 × (4) - 15 = pineapple
8 ÷ 2 × (4) - 15= pineapple
4 × (4) - 15 = pineapple
16 - 15 = pineapple
1 = pineapple
July 8th, 2023 at 5:50:37 AM
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Quote: ChesterDog
1
apple + apple + apple = 6
3 × apple = 6
apple = 2
1 + apple = lemon
1 + 2 = lemon
3 = lemon
apple + lemon = banana
2 + 3 = banana
5 = banana
banana + banana + banana = orange
5 + 5 + 5 = orange
15 = orange
apple lemon ÷ apple × (apple + apple) - orange = pineapple
23 ÷ 2 × (2 + 2) - 15 = pineapple
23 ÷ 2 × (4) - 15 = pineapple
8 ÷ 2 × (4) - 15= pineapple
4 × (4) - 15 = pineapple
16 - 15 = pineapple
1 = pineapple
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Thank you for the confirmation! I'm ready to make this the next viral Facebook puzzle.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 9th, 2023 at 6:21:31 AM
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Quote: WizardQuote: ChesterDog
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I agree! Don, you were close, just the sign was off.
link to original post
The equation is the integral over x = -PI/4 to PI/4 of e^(-ix) dx
= e^(-i PI/4) / (-i) - e^(-i (-PI/4)) / (-i)
= -i * (1 / (e^(i PI/4) - 1 / e^(i (-PI/4)))
...and there's the problem: the last time I checked, 1 / (-i) = i, not -i
July 9th, 2023 at 9:26:33 PM
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Quote: Wizard
The cat =20
the eggs =3
The bananas =6
So the last line = 20+ 3 x 6 = 38
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
July 9th, 2023 at 9:52:51 PM
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Quote: gordonm888
The cat =20
the eggs =3
The bananas =6
So the last line = 20+ 3 x 6 = 38
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Sorry, that is not correct. If it makes you feel better, I made the same mistake you did, initially.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 9th, 2023 at 9:53:50 PM
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In other news, my next newsletter is rather mathematical. I'd appreciate much any comments or corrections.
Draft of July 15, 2023 neswletter.
Thank you!
Draft of July 15, 2023 neswletter.
Thank you!
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 9th, 2023 at 11:44:28 PM
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Quote: WizardThe correct way to evaluate this one is:
7 + 7 ÷ 7 + 7 × 7 – 7 = 7 + 1 + 7 × 7 – 7 because you division supersedes addition and multiplication and is
to the left of multiplication
If I'm following this correctly...
7 + 7 ÷ 7 + 7 × 7 – 7 = 7 + 1 + 7 × 7 – 7 because you division supersedes addition, and multiplication >division< and is
to the left of multiplication
[edit] Maybe it's...
7 + 7 ÷ 7 + 7 × 7 – 7 = 7 + 1 + 7 × 7 – 7 because you division supersedes addition and multiplication and is
to the left of multiplication
Last edited by: Gialmere on Jul 10, 2023
Have you tried 22 tonight? I said 22.
July 10th, 2023 at 12:20:07 AM
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Quote: WizardIn other news, my next newsletter is rather mathematical. I'd appreciate much any comments or corrections.
Draft of July 15, 2023 neswletter.
Thank you!
link to original post
Wiz,
You used two acronyms: PEMDAS and PEDMAS. To be consistent with your mnemonic, you should stick to PEMDAS.
Also, for your first problem you initially say that 9 is wrong, but then later you give the answer as 9. I suspect you meant to say: "If you got the answer of 1, you are wrong", because you later demonstrate that 1 is incorrect.
Hope this helps!
Dog Hand
July 10th, 2023 at 5:36:29 AM
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Wiz,
Your order of operations newsletter does not mention the "unary functions" such as the "unary minus" operation. For example, for a real number x what is the correct value for
-x² = ?
Is this interpreted as -(x²) < 0 or as (-x)² > 0?
Insert Jeopardy theme here.
I was taught that "unary functions" (besides minus, other unary functions include trig functions, factorial, and absolute value) come right after Parentheses in the order of operations, so the correct answer is (-x)² and the result is positive.
On the other hand,
0 - 2² = -4
Because here the - is a binary function, so the operation falls to the AS portion.
Comments?
Dog Hand
Your order of operations newsletter does not mention the "unary functions" such as the "unary minus" operation. For example, for a real number x what is the correct value for
-x² = ?
Is this interpreted as -(x²) < 0 or as (-x)² > 0?
Insert Jeopardy theme here.
I was taught that "unary functions" (besides minus, other unary functions include trig functions, factorial, and absolute value) come right after Parentheses in the order of operations, so the correct answer is (-x)² and the result is positive.
On the other hand,
0 - 2² = -4
Because here the - is a binary function, so the operation falls to the AS portion.
Comments?
Dog Hand
July 10th, 2023 at 7:00:08 AM
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It's easy Monday. Time for another triad of trifling tricksies...
Point A is the center of one square and the vertex of another. The side of each square is 4 inches.
What is the area of the shaded region?
How dey doo dat?
The day before yesterday, Timmy was 13 years old. Next year he’ll be 16.
What is his birthday, and what is today’s date?
Point A is the center of one square and the vertex of another. The side of each square is 4 inches.
What is the area of the shaded region?
How dey doo dat?
The day before yesterday, Timmy was 13 years old. Next year he’ll be 16.
What is his birthday, and what is today’s date?
Have you tried 22 tonight? I said 22.
July 10th, 2023 at 8:55:30 AM
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See the diagram, the shaded triangles (ABC ADE) are identical, so have the same area. Thus the yellow area (ACPDE) has the same area as the 2"x2" square ABRD. Hence the area is 4 sq".
Taps: I knew this one, but you can also see this and other illusions at https://www.optical-illusionist.com/illusion/101/floating-tap-illusion/
If today is 1st Jan and the person was 14 on 31st December, then on 30th December they would have been 13; also on 31st December this year they'll be 15, so next year they'll be 16.
Interesting puzzle, which appeared on TV here on ITV (UK), which month is longest January, August or October?
July 10th, 2023 at 10:13:28 AM
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Quote: gordonm888Quote: Wizard
The cat =20
the eggs =3
The bananas =6
So the last line = 20+ 3 x 6 = 38
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Oooh I see. On the fourth line there are only two eggs in a nest and 4 bananas in a clump. So the the answer is
20 + 4 x 2 = 28
as ThatDonGuy has so righteously responded,
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
July 10th, 2023 at 10:52:20 AM
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Quote: gordonm888Quote: gordonm888Quote: Wizard
The cat =20
the eggs =3
The bananas =6
So the last line = 20+ 3 x 6 = 38
I get 26.
20+1+1+1+1+1+1
,
At my age, a "Life In Prison" sentence is not much of a deterrent.
July 10th, 2023 at 12:11:21 PM
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Thank you Gialmere and DogHand for your corrections!
I welcome correction on this and have not seen any such questions on FB. That said, I interpret -x² as -(x²). In other words, you evaluate the exponent first. If I wanted to convey -x squared, I would write it as (-x)².
In all these things, I also consider how things are presented.
Again, I welcome correction.
Quote: DogHandWiz,
Your order of operations newsletter does not mention the "unary functions" such as the "unary minus" operation. For example, for a real number x what is the correct value for
-x² = ?
Is this interpreted as -(x²) < 0 or as (-x)² > 0?
Insert Jeopardy theme here.
I was taught that "unary functions" (besides minus, other unary functions include trig functions, factorial, and absolute value) come right after Parentheses in the order of operations, so the correct answer is (-x)² and the result is positive.
On the other hand,
0 - 2² = -4
Because here the - is a binary function, so the operation falls to the AS portion.
Comments?
Dog Hand
link to original post
I welcome correction on this and have not seen any such questions on FB. That said, I interpret -x² as -(x²). In other words, you evaluate the exponent first. If I wanted to convey -x squared, I would write it as (-x)².
In all these things, I also consider how things are presented.
Again, I welcome correction.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 10th, 2023 at 12:53:01 PM
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Quote: DRichQuote: gordonm888Quote: gordonm888Quote: Wizard
The cat =20
the eggs =3
The bananas =6
So the last line = 20+ 3 x 6 = 38
I get 26.
20+1+1+1+1+1+1
,
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Isn't that a multiply rather than an add between the eggs and bananas?
May the cards fall in your favor.
July 10th, 2023 at 4:24:38 PM
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Quote: Dieter
Isn't that a multiply rather than an add between the eggs and bananas?
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Yes.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 10th, 2023 at 4:31:57 PM
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Quote: GialmereIt's easy Monday. Time for another triad of trifling tricksies...
Point A is the center of one square and the vertex of another. The side of each square is 4 inches.
What is the area of the shaded region?
How dey doo dat?
The day before yesterday, Timmy was 13 years old. Next year he’ll be 16.
What is his birthday, and what is today’s date?
link to original post
I would include an answer for Geometry, but I have seen this before, and charliepatrick answered it the way I would have.
There's a pipe running up from the ground to the spout that's hidden by the water coming down that surrounds it.
If today is 1/1, then yesterday is 12/31 of last year. If that was Timmy's 15th birthday, then he was 14 two days ago. On 12/31 of next year, he will be 16.
July 10th, 2023 at 4:37:13 PM
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Quote: charliepatrickSee the diagram, the shaded triangles (ABC ADE) are identical, so have the same area. Thus the yellow area (ACPDE) has the same area as the 2"x2" square ABRD. Hence the area is 4 sq".
Taps: I knew this one, but you can also see this and other illusions at https://www.optical-illusionist.com/illusion/101/floating-tap-illusion/Easy puzzle, how to make Sundays longer and Mondays shorter, thay up late (e.g. watching baseball or NFL overnight) and get up late!!If today is 1st Jan and the person was 14 on 31st December, then on 30th December they would have been 13; also on 31st December this year they'll be 15, so next year they'll be 16.
Interesting puzzle, which appeared on TV here on ITV (UK), which month is longest January, August or October?
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Correct!
Good show.
Another way to do it is to add more squares. No matter the orientation of the second square, adding three contiguous squares as shown will divide the first square into four equal regions. Each region is then one-fourth of the square’s total area, or 4 square inches.
Far be it for me to reveal how a magic trick is done. If, however, you solved it, then you might also be able to solve how the famous Indian levitation trick is done...
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Quote: charliepatrickInteresting puzzle, which appeared on TV here on ITV (UK), which month is longest January, August or October?
I've lost track of what's in play on this thread but will take a stab at this one. I can see it varying depending on the asker's intent but, for the US, I'll go with October. Since daylight savings ends, October lasts for 31 days + 1 hour.
Have you tried 22 tonight? I said 22.
July 10th, 2023 at 4:39:09 PM
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Quote: ThatDonGuyQuote: GialmereIt's easy Monday. Time for another triad of trifling tricksies...
Point A is the center of one square and the vertex of another. The side of each square is 4 inches.
What is the area of the shaded region?
How dey doo dat?
The day before yesterday, Timmy was 13 years old. Next year he’ll be 16.
What is his birthday, and what is today’s date?
link to original post
I would include an answer for Geometry, but I have seen this before, and charliepatrick answered it the way I would have.
There's a pipe running up from the ground to the spout that's hidden by the water coming down that surrounds it.
If today is 1/1, then yesterday is 12/31 of last year. If that was Timmy's 15th birthday, then he was 14 two days ago. On 12/31 of next year, he will be 16.
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ThatDonGuy weighs in correctly just under the wire.
Have you tried 22 tonight? I said 22.
July 10th, 2023 at 5:09:05 PM
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Absolutely correct. (I couldn't remember whether the US went in the same month, and in some places the clocks don't change. Hence I was going to ask why December 2016 was longer than December 2017.)Quote: Gialmere...
Quote: charliepatrickInteresting puzzle, which appeared on TV here on ITV (UK), which month is longest January, August or October?
I've lost track of what's in play on this thread but will take a stab at this one. I can see it varying depending on the asker's intent but, for the US, I'll go with October. Since daylight savings ends, October lasts for 31 days + 1 hour.
This is leap seconds - see https://en.wikipedia.org/wiki/Leap_second
July 10th, 2023 at 5:26:52 PM
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Quote: charliepatrickAbsolutely correct.
I never grow tired of those words.
Unfortunately D'oh! I just realized I got it right for the wrong reasons. In the US they pushed the end of daylight savings into November around 10 years ago. I just grew up with it always ending the last full weekend of October (just in time for Halloween) and still think of it in those terms. November only has 30 days so I guess we yanks will have to settle for the occasional leap second in December.
Last edited by: Gialmere on Jul 10, 2023
Have you tried 22 tonight? I said 22.
July 11th, 2023 at 7:00:03 AM
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It's Toughie Tuesday. Let us consider a rather ruthless radical...
Can you find N in simplest form?
Can you find N in simplest form?
Have you tried 22 tonight? I said 22.
July 11th, 2023 at 8:06:24 AM
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Quote: GialmereIt's Toughie Tuesday...
Can you find N in simplest form?
I can see that (SQRT(2)-1)2=2+1-2*SQRT(2)=3-2*SQRT(2). Hence the value after the minus is SQRT(2)-1. Using a calculator I can see that N=1, but I can't see a similar approach to prove the front half is SQRT(2). I suspect there's an (a-b)(a+b) somewhere!
July 11th, 2023 at 8:21:27 AM
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Quote: GialmereIt's Toughie Tuesday. Let us consider a rather ruthless radical...
Can you find N in simplest form?
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I squared the first term and got 2. So, the first term is the square root of 2.
The second term simplifies to the square root of 2 minus 1.
Subtracting yields 1!
July 11th, 2023 at 8:43:09 AM
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I am not familiar with the PEMDAS order of operations acronym. I learned order of operations while learning to program in BASIC, which was: parentheses first, then multiplication/division left-to-right, then addition/subtraction left-to-right (which to me is more straightforward and much easier to implement than trying to use an acronym). Ironically, my 6th grade teacher tried to teach us that order of operations were: addition, then subtraction, then multiplication, then division!! I tried to correct her, but she would have none of it!Quote: WizardIn other news, my next newsletter is rather mathematical. I'd appreciate much any comments or corrections.
Draft of July 15, 2023 neswletter.
Thank you!
link to original post
However, my evaluation of 6 ÷ 2 (1 + 2) was 1, not 9. This is not because of the acronym, and certainly not because of what Mrs. Metcalf tried to teach us. I have always had the understanding that implied multiplication takes precedence over explicit multiplication/division. E.g., wouldn't we agree the equation 8 ÷ 2x = 2 evaluates to x = 2, not x = 1/2?
I found this article on Stack Exchange. Although it does not definitively decide the matter, it does offer support for both interpretations, including a picture of two Casio calculators showing different evaluations of the expression in question:
Honestly, I can't remember the last time I used the division symbol (÷). It was probably in Mrs. Metcalf's class! On seeing that expression, my brain automatically saw it as:
___6____
2(1 + 2)
And using that kind of notation removes any abmiguity.
"Dealer has 'rock'... Pay 'paper!'"
July 11th, 2023 at 5:35:40 PM
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Quote: charliepatrickI can see that (SQRT(2)-1)2=2+1-2*SQRT(2)=3-2*SQRT(2). Hence the value after the minus is SQRT(2)-1. Using a calculator I can see that N=1, but I can't see a similar approach to prove the front half is SQRT(2). I suspect there's an (a-b)(a+b) somewhere!
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Quote: ChesterDog
I squared the first term and got 2. So, the first term is the square root of 2.
The second term simplifies to the square root of 2 minus 1.
Subtracting yields 1!
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Correct!!
Excellent
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A solid 10, but also imaginary.
Have you tried 22 tonight? I said 22.
July 12th, 2023 at 7:00:04 AM
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A spherical basketball is packed in a cubical box into which it fits exactly.
What percent of the volume of the box is used up by the basketball?
Have you tried 22 tonight? I said 22.
July 12th, 2023 at 4:36:56 PM
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Quote: Gialmere
A spherical basketball is packed in a cubical box into which it fits exactly.
What percent of the volume of the box is used up by the basketball?
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Let r be the radius of the basketball
The volume of the ball = 4 PI r^3 / 3
The volume of the box = (2r)^3 = 8 r^3
The ratio = 4 PI / 24 = PI / 6
Since you asked for a percent, it is 100 PI / 6 = (50 PI / 3) %
July 12th, 2023 at 5:36:18 PM
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Quote: ThatDonGuy
Let r be the radius of the basketball
The volume of the ball = 4 PI r^3 / 3
The volume of the box = (2r)^3 = 8 r^3
The ratio = 4 PI / 24 = PI / 6
Since you asked for a percent, it is 100 PI / 6 = (50 PI / 3) %
link to original post
Correct!
Well done.
Yes, it only occupies a little over 52% of the space. That's a lot of wasted cardboard, and is one of the reasons why balls are usually packaged in this manner...
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Basketballs bounce when you drop them.
Have you tried 22 tonight? I said 22.
July 13th, 2023 at 6:23:52 AM
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When I was much younger than I am today we were taught to solve equations from left to right regardless of the function. This is obviously wrong but was used in schools to get students use to working with numbers.
Then we were introduced to BODMAS which means Brackets of Division, Multiplication, Addition and Subtraction, in that order. Using this 6/2(1+2) = 1 but 6/2*3 = 9 which shows the difference brackets make.
Today, I use a HP50g Graphing Calculator which uses reverse Polish notation and stack architecture and both answers can be obtained depending on the readers interpretation of the problem.
Then we were introduced to BODMAS which means Brackets of Division, Multiplication, Addition and Subtraction, in that order. Using this 6/2(1+2) = 1 but 6/2*3 = 9 which shows the difference brackets make.
Today, I use a HP50g Graphing Calculator which uses reverse Polish notation and stack architecture and both answers can be obtained depending on the readers interpretation of the problem.
Casino Enemy No.1
July 13th, 2023 at 7:00:02 AM
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The earth is being invaded by outer space predators. A defending army squad has six shooters. The first shooter hits his target with a probably of 49%. The second hits with 75%. Then with 41%, 20%, 34% and 63% respectively.
What is the probability of a target hit if the entire squad shoots at the same attacking predator all at once?
Have you tried 22 tonight? I said 22.
July 13th, 2023 at 7:20:00 AM
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Quote: GialmereQuote: ThatDonGuy
Let r be the radius of the basketball
The volume of the ball = 4 PI r^3 / 3
The volume of the box = (2r)^3 = 8 r^3
The ratio = 4 PI / 24 = PI / 6
Since you asked for a percent, it is 100 PI / 6 = (50 PI / 3) %
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Correct!
Well done.Yes, it only occupies a little over 52% of the space. That's a lot of wasted cardboard, and is one of the reasons why balls are usually packaged in this manner...
----------------------------------------Basketballs bounce when you drop them.
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Your comment does not make any sense. Why not just deflate the basketball first and then pack it? When people have stomach inflation, they usually make themselves comfortable by releasing their gas.
July 13th, 2023 at 8:46:46 AM
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Quote: GialmereWhat is the probability of a target hit if the entire squad shoots at the same attacking predator all at once?
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98.53%
First I calculate the probability of none of the shooters hitting their target. The probability of a shooter missing is obviously (1 - their hit probability). So, take the product of all miss probabilities (.51 x .25 x .59 x .80 x .66 x .37 = 0.0147). The probability of at least one shooter hitting, is (1 - "all miss probability"). So, 1 - 0.0147 = 0.9853 or 98.53% chance the predator is hit.
First I calculate the probability of none of the shooters hitting their target. The probability of a shooter missing is obviously (1 - their hit probability). So, take the product of all miss probabilities (.51 x .25 x .59 x .80 x .66 x .37 = 0.0147). The probability of at least one shooter hitting, is (1 - "all miss probability"). So, 1 - 0.0147 = 0.9853 or 98.53% chance the predator is hit.
Predator was one of two movies released in 1987 to feature two future US state governors. For 10 points, what is the other movie? Get a bonus of 25 points if you can also name the future governors.
Last edited by: Joeman on Jul 13, 2023
"Dealer has 'rock'... Pay 'paper!'"
July 13th, 2023 at 7:31:14 PM
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Quote: Joeman98.53%
First I calculate the probability of none of the shooters hitting their target. The probability of a shooter missing is obviously (1 - their hit probability). So, take the product of all miss probabilities (.51 x .25 x .59 x .80 x .66 x .37 = 0.0147). The probability of at least one shooter hitting, is (1 - "all miss probability"). So, 1 - 0.0147 = 0.9853 or 98.53% chance the predator is hit.
Correct!
Nice shooting.
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I'll be returning.
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Quote: JoenmaPredator was one of two movies released in 1987 to feature two future US state governors. For 10 points, what is the other movie? Get a bonus of 25 points if you can also name the future governors.
Without looking it up, I'm guessing "The Running Man" which, like "Predator," also featured future California govenator Ahnold and non-party affiliated future governor of Minnisota, Jesse "The Body" Ventura.
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Quote: acesideYour comment does not make any sense. Why not just deflate the basketball first and then pack it? When people have stomach inflation, they usually make themselves comfortable by releasing their gas.
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It reminds of the original Star Trek show. In a production meeting, Gene Roddenberry was asked that since the Enterprise crew were always falling out of their chairs, why not give them seat belts? He immediately replied that they can't give them seat belts because, if they did, the crew couldn't fall out of their chairs.
Last edited by: Gialmere on Jul 14, 2023
Have you tried 22 tonight? I said 22.
July 13th, 2023 at 10:22:12 PM
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A study of one billion email accounts shows that they received an average of four spam emails within 24 hours of creating the account, sixteen spams within 48 hours and thirty-six spams within 72 hours.
Assuming the aforementioned growth rate is continuous, starts the instant an account is opened and never ends, what’s the expected waiting time for a new account to receive its first spam ?
Assuming the aforementioned growth rate is continuous, starts the instant an account is opened and never ends, what’s the expected waiting time for a new account to receive its first spam ?
It’s all about making that GTA
July 14th, 2023 at 6:48:47 AM
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The average number of spams in t hours is 4 t^2.
This = 1 when t = 1/2, so the expected waiting time for the first spam is 30 minutes.
July 14th, 2023 at 2:18:31 PM
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Quote: GialmereQuote: JoemanPredator was one of two movies released in 1987 to feature two future US state governors. For 10 points, what is the other movie? Get a bonus of 25 points if you can also name the future governors.Without looking it up, I'm guessing "The Running Man" which, like "Predator," also featured future California govenator Ahnold and non-party affiliated future governor of Minnisota, Jesse "The Body" Ventura.
All correct for full points!
"Dealer has 'rock'... Pay 'paper!'"
July 14th, 2023 at 5:30:13 PM
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Quote: Ace2A study of one billion email accounts shows that they received an average of four spam emails within 24 hours of creating the account, sixteen spams within 48 hours and thirty-six spams within 72 hours.
Assuming the aforementioned growth rate is continuous, starts the instant an account is opened and never ends, what’s the expected waiting time for a new account to receive its first spam ?
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Good question!
3 hours
I show the average spams after t days to be 4*t^2.
Using the Poisson distribution, the probability of zero spams in t days is exp(-4t^2)*exp(0)/0! = exp(-4t^2).
To get the average time until the first spam, we integrate from 0 to infinity of t*exp(-4*t^2) dt. The answer to this is 1/8. So 1/8 of a day. Since the question was expressed in hours, 24/8=3 hours.
Again, dang good problem. I hope my answer is right.
I'll probably make an Ask the Wizard question out if it. I think I'll change the wording to opening a Facebook account and the time until the first ad for fake stamps.
Last edited by: Wizard on Jul 14, 2023
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 15th, 2023 at 2:14:32 PM
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Quote: WizardQuote: Ace2A study of one billion email accounts shows that they received an average of four spam emails within 24 hours of creating the account, sixteen spams within 48 hours and thirty-six spams within 72 hours.
Assuming the aforementioned growth rate is continuous, starts the instant an account is opened and never ends, what’s the expected waiting time for a new account to receive its first spam ?
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Good question!
3 hours
I show the average spams after t days to be 4*t^2.
Using the Poisson distribution, the probability of zero spams in t days is exp(-4t^2)*exp(0)/0! = exp(-4t^2).
To get the average time until the first spam, we integrate from 0 to infinity of t*exp(-4*t^2) dt. The answer to this is 1/8. So 1/8 of a day. Since the question was expressed in hours, 24/8=3 hours.
Again, dang good problem. I hope my answer is right.
I'll probably make an Ask the Wizard question out if it. I think I'll change the wording to opening a Facebook account and the time until the first ad for fake stamps.
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Disagree.
But you are definitely on the right track with your method.
Using your correct formula of 4*t^2, you can easily calculate that the average number of spams after 3 hours is 0.0625 and also that the average number of spams after 12 hours is 1 (not the same thing as expected time for first spam since the rate is variable). Considering those averages, does your answer of 3 hours seem reasonable to you ?
Incidentally, I prefer to calculate the average number of spams received as t^2 with t as 12-hour periods, but just a preference
But you are definitely on the right track with your method.
Using your correct formula of 4*t^2, you can easily calculate that the average number of spams after 3 hours is 0.0625 and also that the average number of spams after 12 hours is 1 (not the same thing as expected time for first spam since the rate is variable). Considering those averages, does your answer of 3 hours seem reasonable to you ?
Incidentally, I prefer to calculate the average number of spams received as t^2 with t as 12-hour periods, but just a preference
Last edited by: Ace2 on Jul 15, 2023
It’s all about making that GTA
July 15th, 2023 at 3:06:40 PM
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Quote: ThatDonGuy
The average number of spams in t hours is 4 t^2.
This = 1 when t = 1/2, so the expected waiting time for the first spam is 30 minutes.
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The average number of spams in t days is 4 t^2.
This = 1 when t = 1/2, so the expected waiting time for the first spam is 12 hours.
