Easy math puzzles
Poll
 | 21 votes (46.66%) | ||
| | 14 votes (31.11%) | ||
| | 6 votes (13.33%) | ||
| | 2 votes (4.44%) | ||
| | 12 votes (26.66%) | ||
| | 3 votes (6.66%) | ||
| | 6 votes (13.33%) | ||
| | 5 votes (11.11%) | ||
| | 12 votes (26.66%) | ||
| | 10 votes (22.22%) |
45 members have voted
September 13th, 2023 at 6:44:04 AM
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After proposing my solution I did stumble across a 163-ticket wheel - http://lottery.merseyworld.com/Wheel/Wheel.html but it's confusing as the next page then looks at 57.Quote: ThatDonGuy...I vaguely remember somebody posting a 40-ticket solution to a 6/49 game that guaranteed at least one number would have at least 3 hits....
September 13th, 2023 at 7:00:03 AM
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Newspapers in 1944 noted a striking coincidence:
Is this a bizarre, numerical quirk, or can it be explained?
Is this a bizarre, numerical quirk, or can it be explained?
Have you tried 22 tonight? I said 22.
September 13th, 2023 at 7:41:15 AM
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Using the above idea one could divide the range into three parts
(i) 1-14 (ii) 15-28 (iii) 28-37.
Thus given there are five winnings numbers there are either two in (i) or two in (ii) or three in (iii).
The latter can be covered by the lines 28-32 and 33-37 since at least one row must have two.
I've yet to check this but the numbers 1 thru 14 can be covered with 13 lines as follows:-
(it uses the logic used above, have 1-2 with all the remaining numbers 3-14, similarly 3-4 with 5 to 14, then 5-6 with 7 to 14, then do the rest somehow. Mirror logic suggests it could start 1-5 and end 10-14, I don't know )
There might be a way to bring this down to twelve lines, for instance 7 8 appear together a lot, but I don't know.
1 2 3 4 5
1 2 6 7 8
1 2 9 10 11
1 2 12 13 14
3 4 6 7 12
3 4 8 9 13
3 4 10 11 14
5 6 7 8 13
5 6 9 10 14
5 6 8 11 12
7 8 10 11 14
7 9 11 12 13
10 12 13 any any
This give 13 lines to find any pair of numbers in 1-14.
Do the same for 15-28 (you probably only need one or two lines fewer as you don't need to cover No 28 but only 15-27; there may also be a smart way to use 10 12 13 any any etc. across the boundary.)
Thus this currently gives 13 (for 1-14) + 13 (for 15-28) + 2 (for 28-32 and 33-37), giving 28. But I suspect a few more lines can be removed.
(i) 1-14 (ii) 15-28 (iii) 28-37.
Thus given there are five winnings numbers there are either two in (i) or two in (ii) or three in (iii).
The latter can be covered by the lines 28-32 and 33-37 since at least one row must have two.
I've yet to check this but the numbers 1 thru 14 can be covered with 13 lines as follows:-
(it uses the logic used above, have 1-2 with all the remaining numbers 3-14, similarly 3-4 with 5 to 14, then 5-6 with 7 to 14, then do the rest somehow. Mirror logic suggests it could start 1-5 and end 10-14, I don't know )
There might be a way to bring this down to twelve lines, for instance 7 8 appear together a lot, but I don't know.
1 2 3 4 5
1 2 6 7 8
1 2 9 10 11
1 2 12 13 14
3 4 6 7 12
3 4 8 9 13
3 4 10 11 14
5 6 7 8 13
5 6 9 10 14
5 6 8 11 12
7 8 10 11 14
7 9 11 12 13
10 12 13 any any
This give 13 lines to find any pair of numbers in 1-14.
Do the same for 15-28 (you probably only need one or two lines fewer as you don't need to cover No 28 but only 15-27; there may also be a smart way to use 10 12 13 any any etc. across the boundary.)
Thus this currently gives 13 (for 1-14) + 13 (for 15-28) + 2 (for 28-32 and 33-37), giving 28. But I suspect a few more lines can be removed.
September 13th, 2023 at 7:44:56 AM
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Quote: GialmereNewspapers in 1944 noted a striking coincidence:
Is this a bizarre, numerical quirk, or can it be explained?
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It can be explained because the first two numbers (assuming it's 31st December or similar) of your current age and birth year will always add up to the current year. Similarly for something happened (took office) and time since that happened (years in office). And 3888 is twice 1944.
September 13th, 2023 at 9:15:04 AM
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Quote: GialmereNewspapers in 1944 noted a striking coincidence:
Is this a bizarre, numerical quirk, or can it be explained?
link to original post
There are magic tricks based on this principle.
As was pointed out, the first two numbers will sum to 1944 for everybody who was alive in 1944.
The second two will always sum to 1944 for everyone "in office" at that time.
I personally don't do this magic trick because I find it obvious how it's done, but maybe I should try it and see how it goes.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
September 13th, 2023 at 9:15:19 AM
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If one splits the range into 1-9, 10-18, 19-27, 28-37 then there are nine numbers in the first three groups and ten in the last. There must be at least two winning numbers in one of the blocks. Using the same logic there are five lines to cover 9 numbers.
1 2 3 5 8
1 2 3 6 7
1 2 3 4 9
4 5 6 7 8
5 6 7 8 9
I've quickly look at the last group and get seven lines
28 29 30 31 32
28 29 33 34 35
28 29 xx 36 37
30 31 32 33 34
30 31 35 36 37
xx 32 35 36 37
33 34 35 36 37
Hence this gives 5+5+5+7=22 lines.
(I haven't double checked this covers everything, but I think four blocks is a reasonable plan of attack.)
1 2 3 5 8
1 2 3 6 7
1 2 3 4 9
4 5 6 7 8
5 6 7 8 9
I've quickly look at the last group and get seven lines
28 29 30 31 32
28 29 33 34 35
28 29 xx 36 37
30 31 32 33 34
30 31 35 36 37
xx 32 35 36 37
33 34 35 36 37
Hence this gives 5+5+5+7=22 lines.
(I haven't double checked this covers everything, but I think four blocks is a reasonable plan of attack.)
September 13th, 2023 at 10:21:53 AM
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Quote: WizardQuote: GialmereNewspapers in 1944 noted a striking coincidence:
Is this a bizarre, numerical quirk, or can it be explained?
link to original post
There are magic tricks based on this principle.
As was pointed out, the first two numbers will sum to 1944 for everybody who was alive in 1944.
The second two will always sum to 1944 for everyone "in office" at that time.
I personally don't do this magic trick because I find it obvious how it's done, but maybe I should try it and see how it goes.
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Good point! Hitler became the chancellor of germany January 30, 1933
September 13th, 2023 at 12:03:45 PM
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Quote: charliepatrickIf one splits the range into 1-9, 10-18, 19-27, 28-37 then there are nine numbers in the first three groups and ten in the last. There must be at least two winning numbers in one of the blocks. Using the same logic there are five lines to cover 9 numbers.
1 2 3 5 8
1 2 3 6 7
1 2 3 4 9
4 5 6 7 8
5 6 7 8 9
I've quickly look at the last group and get seven lines
28 29 30 31 32
28 29 33 34 35
28 29 xx 36 37
30 31 32 33 34
30 31 35 36 37
xx 32 35 36 37
33 34 35 36 37
Hence this gives 5+5+5+7=22 lines.
(I haven't double checked this covers everything, but I think four blocks is a reasonable plan of attack.)
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Very good work there. It certainly humbles me. I've gone through and can't find a way to do better than 5 tickets with 9 numbers and 7 with 10.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
September 13th, 2023 at 5:42:44 PM
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Quote: charliepatrickIt can be explained because the first two numbers (assuming it's 31st December or similar) of your current age and birth year will always add up to the current year. Similarly for something happened (took office) and time since that happened (years in office). And 3888 is twice 1944.
link to original post
Correct!!
Quote: WizardThere are magic tricks based on this principle.
As was pointed out, the first two numbers will sum to 1944 for everybody who was alive in 1944.
The second two will always sum to 1944 for everyone "in office" at that time.
I personally don't do this magic trick because I find it obvious how it's done, but maybe I should try it and see how it goes.
link to original post
Correct!!
Good show.
This works for any group of people — as long as they’re all still alive and working, these values will add to a miraculous constant. Here, for example, is the Supreme Court in 2009:
Their magic total, sure enough, is just twice 2009.
Their magic total, sure enough, is just twice 2009.
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We have a picture of him in uniform with two lightning bolts on his helmet.
Have you tried 22 tonight? I said 22.
September 13th, 2023 at 6:40:02 PM
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Quote: GialmereGood show.
This works for any group of people — as long as they’re all still alive and working, these values will add to a miraculous constant. Here, for example, is the Supreme Court in 2009:
Their magic total, sure enough, is just twice 2009.
It only "always" works on December 31. Otherwise, if at least one person in the group has already had their birthday/anniversary that year and at least one has not, the numbers will differ by one.
September 14th, 2023 at 7:00:06 AM
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Four of the 8 vertices of a cube are vertices of a regular tetrahedron.
Find the ratio of the surface area of the cube to the surface area of the tetrahedron.
Have you tried 22 tonight? I said 22.
September 14th, 2023 at 7:24:37 AM
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September 14th, 2023 at 5:29:45 PM
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Quote: ChesterDog
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Correct!!
Well done.
It's neat how platonic solids interact. The way a tetrahedron fits into a cube is a good example. It's no wonder that Kepler thought he was discovering God's master plan when he was working with them.
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Have you tried 22 tonight? I said 22.
September 15th, 2023 at 7:00:04 AM
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Take the circumference of the earth at the equator to be 24,000 miles. An airplane taking off at the equator and flying west at 1000 miles an hour would land at exactly the same time that it started. Moreover, the sun would not move in the plane’s sky during the flight.
At what degree of latitude could a plane flying 500 miles per hour keep up with the sun in this way?
Have you tried 22 tonight? I said 22.
September 15th, 2023 at 7:38:32 AM
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60 degrees
September 15th, 2023 at 4:15:14 PM
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I plan to make a future Ask the Wizard question about the Cash 5 Lottery. Here is a preview of my solution.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
September 15th, 2023 at 4:19:56 PM
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Quote: GialmereAt what degree of latitude could a plane flying 500 miles per hour keep up with the sun in this way?
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I get 60 degrees north or south latitude. This is where the circumference is half that of the equator.
As an very unrelated question, how is it that Superman went back in time when he spun around the earth really fast?
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
September 15th, 2023 at 7:26:30 PM
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Quote: aceside60 degrees
link to original post
Quote: WizardI get 60 degrees north or south latitude. This is where the circumference is half that of the equator.
As an very unrelated question, how is it that Superman went back in time when he spun around the earth really fast?
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Correct!
Very good.
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In his book, Sled Driver, SR-71 Blackbird pilot Brian Shul writes:
"I'll always remember a certain radio exchange that occurred one day as Walt (my back-seater) and I were screaming across Southern California 13 miles high. We were monitoring various radio transmissions from other aircraft as we entered Los Angeles airspace. Although they didn't really control us, they did monitor our movement across their scope.
I heard a Cessna ask for a readout of its ground speed."90 knots" Center replied. Moments later, a Twin Beech required the same. "120 knots," Center answered. We weren't the only ones proud of our ground speed that day as almost instantly an F-18 smugly transmitted, "Ah, Center, Dusty 52 requests ground speed readout." There was a slight pause, then the response, "525 knots on the ground, Dusty." Another silent pause.
As I was thinking to myself how ripe a situation this was, I heard a familiar click of a radio transmission coming from my back-seater. It was at that precise moment I realized Walt and I had become a real crew, for we were both thinking in unison. "Center, Aspen 20, you got a ground speed readout for us?" There was a longer than normal pause....
"Aspen, I show 1,742 knots." (That's about 2005 mph)
No further inquiries were heard on that frequency.
"I'll always remember a certain radio exchange that occurred one day as Walt (my back-seater) and I were screaming across Southern California 13 miles high. We were monitoring various radio transmissions from other aircraft as we entered Los Angeles airspace. Although they didn't really control us, they did monitor our movement across their scope.
I heard a Cessna ask for a readout of its ground speed."90 knots" Center replied. Moments later, a Twin Beech required the same. "120 knots," Center answered. We weren't the only ones proud of our ground speed that day as almost instantly an F-18 smugly transmitted, "Ah, Center, Dusty 52 requests ground speed readout." There was a slight pause, then the response, "525 knots on the ground, Dusty." Another silent pause.
As I was thinking to myself how ripe a situation this was, I heard a familiar click of a radio transmission coming from my back-seater. It was at that precise moment I realized Walt and I had become a real crew, for we were both thinking in unison. "Center, Aspen 20, you got a ground speed readout for us?" There was a longer than normal pause....
"Aspen, I show 1,742 knots." (That's about 2005 mph)
No further inquiries were heard on that frequency.
Have you tried 22 tonight? I said 22.
September 22nd, 2023 at 7:18:06 PM
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From the local weekly newspaper here. I posted some of those here before, retyping them, but I finally figured out how to post the pics and link to the solution.
I'm not great with geometry, but even I got this one right (though I did it by a different method than what's described in the answer).
answer
I'm not great with geometry, but even I got this one right (though I did it by a different method than what's described in the answer).
answer
