Next in sequence?
Poll
 | 3 votes (13.63%) | ||
| | 2 votes (9.09%) | ||
| | 14 votes (63.63%) | ||
| | 3 votes (13.63%) |
22 members have voted
January 10th, 2017 at 11:59:32 AM
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So. This is from my Facebook feed. There have been almost 800 answers so far, and none that agree with mine that I've seen. Their most common answers are listed above. So I'm bringing it here, to the experts. I'll post the question; please answer the poll above before you read any responses. I will put my answer in a spoiler tag, and would appreciate you all doing the same.
Fwiw, whoever authored this has not yet confirmed their solution.
1+4=5
2+5=12
3+6=21
8+11=?
Fwiw, whoever authored this has not yet confirmed their solution.
1+4=5
2+5=12
3+6=21
8+11=?
If the House lost every hand, they wouldn't deal the game.
January 10th, 2017 at 12:02:13 PM
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I do not know the author's original intent. But one correct answer is 201, and does not require manipulation of the equations as other solutions above do.
Each equation is in base 10. Each solution is in another base, diminishing by 1.
The first equation is expressed in base 10, answered in base 6. 5 in base 10= 5 in base 6.
The second is expressed in base 10, answered in base 5. 7 in base 10 is 12 in base 5.
The third is expressed in base 10, answered in base 4. 9 in base 10 is 21 in base 4.
The last equation, expressed in base 10, should be answered in base 3, to follow the pattern of previous answers. 19 in base 10 = 201 in base 3.
If the House lost every hand, they wouldn't deal the game.
January 10th, 2017 at 12:10:20 PM
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40. It appears the "total" is the sum of the equation + the prior answer.
Is part of the answer to also come up with the next equation in the sequence?
Simplicity is the ultimate sophistication - Leonardo da Vinci
January 10th, 2017 at 12:14:30 PM
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The pattern appears to be the sum of the first 2 numbers + the result of the previous numbers... Thus:
4 + 7 = 11 (plus previous 21) = 32
5 + 8 = 45
6 + 9 = 60
7 + 10 = 77
8 + 11 = 96
..of course if you're not supposed to extrapolate, then it would be 19 + 21 = 40.
Last edited by: Romes on Jan 10, 2017
Playing it correctly means you've already won.
January 10th, 2017 at 12:18:16 PM
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96
The '+' operator here does not signify addition, but is a more complex operation defined by the following:
a '+' b = (a X b) + a
So:
(1 x 4) + 1 = 5
(2 x 5) + 2 = 12
(3 x 6) + 3 = 21
(8 x 11) + 8 = 96
The '+' operator here does not signify addition, but is a more complex operation defined by the following:
a '+' b = (a X b) + a
So:
(1 x 4) + 1 = 5
(2 x 5) + 2 = 12
(3 x 6) + 3 = 21
(8 x 11) + 8 = 96
"Dealer has 'rock'... Pay 'paper!'"
January 10th, 2017 at 12:20:26 PM
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if you put a plus sign after each sum and consider the shown sums subtotals, to be added as part of the last sum, that works, and the last sum is forty. Next sequence can't guess . I love when I can answer math questions verbally as that is how my brain works LOL.l PS: after looking now, wow are there a bunch of different responses!
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
January 10th, 2017 at 12:23:23 PM
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Quote: Romes
The pattern appears to be the sum of the first 2 numbers + the result of the previous numbers... Thus:
4 + 7 = 11 (plus previous 21) = 32
5 + 8 = 45
6 + 9 = 60
7 + 10 = 77
8 + 11 = 98
..of course if you're not supposed to extrapolate, then it would be 19 + 21 = 40.
Romes, are you saying that:
77+8+11=98
How is that???
January 10th, 2017 at 12:34:06 PM
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Arithmetic error in typing =)...Quote: DocQuote: Romes
The pattern appears to be the sum of the first 2 numbers + the result of the previous numbers... Thus:
4 + 7 = 11 (plus previous 21) = 32
5 + 8 = 45
6 + 9 = 60
7 + 10 = 77
8 + 11 = 98
..of course if you're not supposed to extrapolate, then it would be 19 + 21 = 40.
Romes, are you saying that:77+8+11=98
How is that???
96...
Playing it correctly means you've already won.
January 10th, 2017 at 12:47:40 PM
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Quote: DocQuote: Romes
The pattern appears to be the sum of the first 2 numbers + the result of the previous numbers... Thus:
4 + 7 = 11 (plus previous 21) = 32
5 + 8 = 45
6 + 9 = 60
7 + 10 = 77
8 + 11 = 98
..of course if you're not supposed to extrapolate, then it would be 19 + 21 = 40.
Romes, are you saying that:77+8+11=98
How is that???
Because everything looks like 21 to romes. :)
If the House lost every hand, they wouldn't deal the game.
January 10th, 2017 at 12:52:24 PM
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I voted for 96 and agree with Joeman.
January 10th, 2017 at 12:53:51 PM
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Quote: Ayecarumba40. It appears the "total" is the sum of the equation + the prior answer.
Is part of the answer to also come up with the next equation in the sequence?
I might have titled it poorly. To my understanding, the question is simply to fill in the missing value in the 4th equation.
If the House lost every hand, they wouldn't deal the game.
January 10th, 2017 at 1:02:54 PM
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.Quote: JohnzimboI voted for 96 and agree with Joeman.
Here's the thing. Both 40 and 96 as solutions require you to manipulate the equations . There's no "x" on the left side of the equation, yet people are adding the solution of the previous equation to the next, either by changing the meaning of the addition sign, or by simple extrapolation.
To me, that's like saying 2+2=5 because you add 1 for it being first in the sequence. I see the logic of both progressions, but I think they violate the premise of the question.
Otoh, translating the right sides into a different base is also a manipulation, but it's not a false equivalency. So I think it's the most correct way to solve the problem.
I could be wrong. But that's why I asked the question.
If the House lost every hand, they wouldn't deal the game.
January 10th, 2017 at 1:20:33 PM
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I got what Romes got (after he corrected his arithmetic)
the number to the right of the + is 3 higher than the number on the left of the +
the numbers increment sequentially as you go from line to line
the number to the right of the = is equal to the sum of the numbers to the left of the = plus the answer from the previous line.
extrapolating these things:
the number to the right of the + is 3 higher than the number on the left of the +
the numbers increment sequentially as you go from line to line
the number to the right of the = is equal to the sum of the numbers to the left of the = plus the answer from the previous line.
extrapolating these things:
1 + 4 = 5
2 + 5 = 12
3 + 6 = 21
4 + 7 = 32
5 + 8 = 45
6 + 9 = 60
7 + 10 = 77
8 + 11 = 96
January 10th, 2017 at 1:25:14 PM
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Quote: Dalex64I got what Romes got (after he corrected his arithmetic)
the number to the right of the + is 3 higher than the number on the left of the +
the numbers increment sequentially as you go from line to line
the number to the right of the = is equal to the sum of the numbers to the left of the = plus the answer from the previous line.
extrapolating these things:
1 + 4 = 5
2 + 5 = 12
3 + 6 = 21
4 + 7 = 32
5 + 8 = 45
6 + 9 = 60
7 + 10 = 77
8 + 11 = 96
And I agree with your extrapolation. But none of these equations except the first is true on its own. So how can this be a correct solution?
2 + 5 does not equal 12. Except in translating base higher than 5 to base 5.
If the House lost every hand, they wouldn't deal the game.
January 10th, 2017 at 2:04:59 PM
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Quote: beachbumbabs
And I agree with your extrapolation. But none of these equations except the first is true on its own. So how can this be a correct solution?
2 + 5 does not equal 12. Except in translating base higher than 5 to base 5.
there is also no indication which base the numbers are displayed in, or if that base should be changed between equations, either.
these sorts of problems which appear on facebook and the like tend to redefine what the symbols mean. I think someone mentioned that the answers are a running subtotal, as if you were hitting the subtotal button ⋄ on an adding machine each time you see the = sign.
January 10th, 2017 at 4:15:44 PM
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That's true if + means the binary addition operator, but if + just means "and" and the real phrasing of the question is "1 and 4 = 5; 2 and 5 = 12; etc." then the question can be rephrased as "Here are three datapoints for x, y, and f(x,y). Find f(8,11)." That's relatively easy:Quote: beachbumbabsAnd I agree with your extrapolation. But none of these equations except the first is true on its own. So how can this be a correct solution?
2 + 5 does not equal 12. Except in translating base higher than 5 to base 5.
As has been previously noted, xy+x satisfies f(x,y) for the three datapoints given, and xy+x for x=8 and y=11 is 96. But there are an infinite number of other functions that do as well, so...
I mean, obviously 2+5 does not equal 12, so you can't just take those first three lines at face value or you'd be stuck with "well, 2+5 != 12 so the whole problem is wrong." But IMO it would be dirty pool to create a math problem where the radix changed mid-problem. That'd be like me offering to buy your car for $100000, you agreeing, and then I show up with $32 and demand you hand me the keys.
As is typical with such Internet questions, there isn't enough information given to arrive at a unique solution while discarding all the others.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
January 10th, 2017 at 4:56:25 PM
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The answer is
I can't take credit though. My wife looked at it and had the answer in~ 3 seconds. She can be scary that way.
Whats really weird is that there are multiple algorithms that give the same result (i.e. Romes and Joeman)
96. The algorithm is
resulting in
- Perform multiplication instead of addition and
- add '1' to the second term
resulting in
- 1+4 --> 1*5 = 5
- 2+5 --> 2*6 = 12
- 3+6 --> 3*7 = 21
- 8+11 --> 8*12 = 96
I can't take credit though. My wife looked at it and had the answer in~ 3 seconds. She can be scary that way.
Whats really weird is that there are multiple algorithms that give the same result (i.e. Romes and Joeman)
My goal of being well informed conflicts with my goal of remaining sane.
January 10th, 2017 at 4:58:40 PM
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Quote: beachbumbabs
I do not know the author's original intent. But one correct answer is 201, and does not require manipulation of the equations as other solutions above do.
Each equation is in base 10. Each solution is in another base, diminishing by 1.
The first equation is expressed in base 10, answered in base 6. 5 in base 10= 5 in base 6.
The second is expressed in base 10, answered in base 5. 7 in base 10 is 12 in base 5.
The third is expressed in base 10, answered in base 4. 9 in base 10 is 21 in base 4.
The last equation, expressed in base 10, should be answered in base 3, to follow the pattern of previous answers. 19 in base 10 = 201 in base 3.
1 + 4 = 5 => 5 in base 5
2 + 5 = 7 => 12 in base 5
3 + 6 = 9 => Aimee21 in base 4
8 + 11 = 19 => 103 in base 4
January 10th, 2017 at 5:03:04 PM
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Quote: TumblingBonesThe answer is
96. The algorithm is
- Perform multiplication instead of addition and
- add '1' to the second term
resulting in
- 1+4 --> 1*5 = 5
- 2+5 --> 2*6 = 12
- 3+6 --> 3*7 = 21
- 8+11 --> 8*12 = 96
I can't take credit though. My wife looked at it and had the answer in~ 3 seconds. She can be scary that way.
Given the progression of the first three examples, and the lack of any indication that lines had been skipped, shouldn't the fourth equation in the sequence be "4+7 = 32", not "8+11 = 96"?
Simplicity is the ultimate sophistication - Leonardo da Vinci
January 10th, 2017 at 6:06:30 PM
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Ayecarumba: There seem to be two modes of thought when attacking this problem. Several folks (e.g. yourself, Romes, and beachbumbabs) have taken an approach in which the solution for a given line is in some manner dependent on previous lines. In that case your observation that "a line has been skipped" would be relevant. Other folks (e.g MathExtremist and my significant other) view this as an encryption problem i.e.,
You are perfectly correct that "4+7=32" is another valid datapoint in the set (i.e., f(4,7)=32).
Quote: MathExtremistthe question can be rephrased as "Here are three datapoints for x, y, and f(x,y). Find f(8,11)."
You are perfectly correct that "4+7=32" is another valid datapoint in the set (i.e., f(4,7)=32).
My goal of being well informed conflicts with my goal of remaining sane.
January 10th, 2017 at 6:36:27 PM
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The solution to each equation is the product of the two numbers plus the smaller one. The order of the equations is irrelevant.
1 x 4 + 1 = 5
2 x 5 + 2 = 12
3 x 6 + 3 = 21
8 x 11 + 8 = 96
January 10th, 2017 at 11:53:51 PM
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Using the subtotal method:
x+y = f(x,y) = SUM[x, y, f(x-1, y-1)] where X > 0 OR Y > 0
-3+0 = -3
-2+1 = -1-3 = -4
-1+2 = 1-4 = -3
0+3 = 3-3 = 0
1+4 = 5+0 = 5
2+5 = 7+5 = 12
3+6 = 9+12 = 21
4+7 = 11+21 = 32
5+8 = 13+32 = 45
6+9 = 15+45 = 60
7+10 = 17+60 = 77
8+11 = 19+77 = 96
Using f(x,y) = x*(y+1) method:
f(8,11) = 8*(11+1) = 8*12 = 96
Like ME said -- there are many formulas that lead to the same answer....or that at least follow the pattern.
BTW, 5 does not exist in base 5.
5 in decimal is 10 in base-5: 1*5^1 + 0*5^0 Just like 2 in decimal is 10.
x+y = f(x,y) = SUM[x, y, f(x-1, y-1)] where X > 0 OR Y > 0
-3+0 = -3
-2+1 = -1-3 = -4
-1+2 = 1-4 = -3
0+3 = 3-3 = 0
1+4 = 5+0 = 5
2+5 = 7+5 = 12
3+6 = 9+12 = 21
4+7 = 11+21 = 32
5+8 = 13+32 = 45
6+9 = 15+45 = 60
7+10 = 17+60 = 77
8+11 = 19+77 = 96
Using f(x,y) = x*(y+1) method:
f(8,11) = 8*(11+1) = 8*12 = 96
Like ME said -- there are many formulas that lead to the same answer....or that at least follow the pattern.
BTW, 5 does not exist in base 5.
5 in decimal is 10 in base-5: 1*5^1 + 0*5^0 Just like 2 in decimal is 10.
January 11th, 2017 at 10:16:02 PM
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I think people are overthinking the problem. Sometimes you just have to strike the nail on the head. The answer is 40. Just my opinion.
January 12th, 2017 at 6:44:07 AM
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if there is no official answer, then this math exercise is perfect for the Millennials. Everybody is right and and we all get a trophy for participating!
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
January 12th, 2017 at 6:50:39 AM
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https://www.youtube.com/watch?v=-HFwok9SlQQQuote: odiousgambitif there is no official answer, then this math exercise is perfect for the Millennials. Everybody is right and and we all get a trophy for participating!
Playing it correctly means you've already won.
January 12th, 2017 at 8:37:44 AM
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96.
Each number of the right side of the equation equals x*(y+1), where x is the first number and y is the second.
8*(11+1) = 96
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 12th, 2017 at 8:40:07 AM
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Quote: RSUsing the subtotal method:
x+y = f(x,y) = SUM[x, y, f(x-1, y-1)] where X > 0 OR Y > 0
-3+0 = -3
-2+1 = -1-3 = -4
-1+2 = 1-4 = -3
0+3 = 3-3 = 0
1+4 = 5+0 = 5
2+5 = 7+5 = 12
3+6 = 9+12 = 21
4+7 = 11+21 = 32
5+8 = 13+32 = 45
6+9 = 15+45 = 60
7+10 = 17+60 = 77
8+11 = 19+77 = 96
Using f(x,y) = x*(y+1) method:
f(8,11) = 8*(11+1) = 8*12 = 96
Like ME said -- there are many formulas that lead to the same answer....or that at least follow the pattern.
Thanks for making me feel less than knowledgable. I just looked for a pattern and came up with 96.
January 13th, 2017 at 3:32:13 AM
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Quote: Romeshttps://www.youtube.com/watch?v=-HFwok9SlQQ
[video says there is no 'Millennials' generation ]
I may be stepping on some toes to rag on the M-gen, so from now on I will pick on Generation Z ....... LOL
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
