## Poll

22 members have voted

beachbumbabs
Joined: May 21, 2013
• Posts: 9045
January 10th, 2017 at 12:53:51 PM permalink
Quote: Ayecarumba

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?

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."
beachbumbabs
Joined: May 21, 2013
• Posts: 9045
January 10th, 2017 at 1:02:54 PM permalink
Quote: Johnzimbo

I 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."
Dalex64
Joined: Feb 10, 2013
• Posts: 667
January 10th, 2017 at 1:20:33 PM permalink
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:

`1	+ 4	= 52	+ 5	= 123	+ 6	= 214	+ 7	= 325	+ 8	= 456	+ 9	= 607	+ 10	= 778	+ 11	= 96`

beachbumbabs
Joined: May 21, 2013
• Posts: 9045
January 10th, 2017 at 1:25:14 PM permalink
Quote: Dalex64

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:

`1	+ 4	= 52	+ 5	= 123	+ 6	= 214	+ 7	= 325	+ 8	= 456	+ 9	= 607	+ 10	= 778	+ 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."
Dalex64
Joined: Feb 10, 2013
• Posts: 667
January 10th, 2017 at 2:04:59 PM permalink
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.
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
Thanks for this post from:
January 10th, 2017 at 4:15:44 PM permalink
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.

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:
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
TumblingBones
Joined: Dec 25, 2016
• Posts: 75
January 10th, 2017 at 4:56:25 PM permalink
96. The algorithm is
• 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)
777
Joined: Oct 7, 2015
• Posts: 594
January 10th, 2017 at 4:58:40 PM permalink
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

Ayecarumba
Joined: Nov 17, 2009
• Posts: 5351
January 10th, 2017 at 5:03:04 PM permalink
Quote: TumblingBones

96. The algorithm is
• 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"?
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TumblingBones
Joined: Dec 25, 2016
• Posts: 75
January 10th, 2017 at 6:06:30 PM permalink
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.,
Quote: MathExtremist

the 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).