This came from my son who got it from someone else at school.

I solved it quickly and texted him the answer just as I was getting into my car for work.

He wrote: "Wrong" and sent me a ridiculous solution.

I typed: "Ohh boy, how could you miss it! I will beat you up at home:)" and started driving.

Stuck in traffic I thought back to it and the 99% that are getting it wrong and suddenly realized that his answer is in fact correct!

I texted: "Apology! Now that my head has cooled off I see that you were right."

He wrote: "Hahahahahaha".

No one at my work got it right either. Could you?

There is at least two solutions. Let's call them: my and my son's. Both are kind of correct. But his is more original.

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

## 30 comments:

26?

5=26! 2+5+3=10; 3+10+4=17; 4+17+5=26....

My first thought was to solve it as an algorithm and I got 5=26. x*x+1 (2*2+1=5, 3*3+1=10, 4*4+1=17)

But then, duh! 2=5, so 5=2! Admittedly, my son noticed that answer before me!

5=2; isn't an equal sign reflexive!?

27. Square number; add 1.

Most will answer 26, as the pattern appears to be 1 more than the square of the number. However, if the reflexive property holds, if 2 = 5, then 5 = 2.

The two answers I like are both 26.

Solution #1 is "the square, plus one."

Solution #2 is just the series, +5, +7, and then +9.

I'm going with 26 (x=y2 + 1), which I'm also guessing was your answer.

Well, the trap that you presumably fell into is noticing the pattern in each pair of numbers (call them A and B) - each 'B' number is 1 higher than the square of the 'A' number (so b = a^2 +1).

However, since the first thing we are told is '2 = 5' we therefore know that '5 = 2' ^_^

2 or 26

25 because the pattern is n^2 + 1

2 because an equal sign means that if 2 is equivalent to 5 then 5 must be equivalent to 2.

I don't consider either one of them correct. Either the number system is getting tortured (2 and 5 are not equivalent) or the equal sign is. The whole premise of 2 being the same as 5 or 5 the same as 26 is a disobedience of the standard meaning of =.

But then I belong to the Bah Humbug school of thought. I might even be a charter member.

Solution 1:

5 = 26 (square the number and add 1 to it)

Solution 2:

5 = 2 (from line 1)

Maria.

I imagine that my answer is like yours. I got 19. Each number increases by 5 plus 2 above the preceding one.

Gurubandhu

I solved it as 26. If you look at the sequence, the answer seems to be adding the previous equations numbers, plus the current equations number i.e. 2 = 5, 3 = 10 (2+3+5), 4=17 (3+4+10), 5 = 26 (4+5+17).

Showing this to my 11 yo, he said that 5 = 2 because it said it in the first equality.

adult answer = 26

kid answer = 2

I would be tempted to say that since the first line states 2=5, we should also have 5=2.

5 could equal 2 since you already said that once. But the next number could also be 26 since each number on the right is obtained by adding the two numbers on the left to it. 10 = 5 +(2+3), 17 = 10 + (3+4), so 26 = 17 + (4+5).

So 2 or 26, take your pick.

My answer is 26. And I got it by squaring the first number plus one.

Jessica K. via email

Kim via email:

Hi Maria,

Been busy, but saw today's email, and gave it a look. Plus, I see Ilya (who I know) is only one answer behind me!

I posted online, but I seem to recall that when I was doing these every week, my posts didn't always go through, so here's my answer:

26. In each case, the number to the right of the equals sign = the sum of the numbers in the equation above it and the number to the left of the equals sign (e.g., 2+5+3 = 10; 3+10+4=17, so 4+17+5=26)

BTW, my answer is also works for x^2+1.

Which is not a coincidence.

What we have is:

x --> x^2 + 1

so the next line is x+1 --> (x+1)^2 + 1 = x^2 + 2x + 2

and it would also equal (summing the three components), x + x^2 + 1 + (x+1) -> x^2 + 2x + 2!

So, I'm assuming that's what you got. What did your son get?

a bit later in another email:

WAIT! Got your son's answer!

The number on the left side is the number of prime numbers to add.

The first five prime numbers are 2, 3, 5, 7, 11

N sum of first n prime numbers

2 5

3 10

4 17

5 28

and a few hours later:

Still thinking about you. I have one other possible answer, and I bet THIS is your son's:

We know from the first equation that 2=5. Therefore, 5=2.

I keep coming up with 26.

A. If the column on the right is the addition of progression of odd numbers, starting with +5, then +7, the next would be 17+9, or 26.

B. If the pattern is Y=X^2 +1, then 5^2 + 1 is 26.

I tried both directions in attempting to come to the sums of each number; the horizontal and the vertical summations. The horizontal attempt fell through as I could not establish a pattern, but vertically, travelling downward from each number to the next I did see a pattern. The answer is 5 = 26. I noticed that from sum 5 to sum 10 were 5 steps or increments and from sum 10 to sum 17 were 7 steps or increments. Following through to arrive at the answer of 26 I added 9 steps or increments to 17. I knew this was correct because then testing the theory by noticing that there are 2 increments between 5 and 7 increments, it is logical to assume that there is also 2 more increments, to make the steps look like 5,7 and 9. Then 9 is correct by adding 17 to 9 equals 26.

The notation with equality sign is somewhat strange, I interpreted it as "function of", i.e. F(2)=5, etc. One solution that fits is F(x)=x*x+1, leading to F(5)=26.

My first answer is 26. All the numbers are squared and increased by 1.

While trying to think of another answer, the only one that makes sense at the moment is: if 2 = 5 then 5 should be equal to 2.

Lulu

I would say there are two answers:

If it is looked at as a progression then the answer would be 26. (Add 5, then 7, then 9).

If each statement is looked at as a separate fact, then the answer would be 2, 2=5, so 5= 2!

Ok. As you see there are two very different answers. 26 and 2.

The easier one is 2 and it is harder to find it. But it is written up there on the first line that 2=5, so it should be that 5=2.

2 = 5

3 = 10

4 = 17

5 = ?

We see that mathematically it is wrong because 2 is not equal to 5 etc. So someone is lying: either numbers or the "=" sign. We are either in a kingdom where = is not equal but more like correspondence sign but numbers are real numbers. Or we are in a kingdom where numbers are not what we expect them to be but "=" is equal.

In the first kingdom, we all rushed to find the pattern that led us to the answer 26. And there are a few ways to find it!

In the second kingdom , "=" is "=" and if 2=5 then 5=2!

Pretty amazing that quite a few of you saw both answers. It is very difficult to change state of mind and move between those kingdoms. Those who got both answers will receive 2 puzzle points, those who got one will receive 1 point.

Gurubandhu - I am sorry but I do not understand the 19th. Your solution still comes to 26 if I understood it correctly.

Have a great week!

I have to confess that I never would have found the reflexive property had you not said there were 2 answers. These problems you come up with are just wonderful even if I do crab about them sometimes.

32

If 2=5

then 5=2

If 2=5

Then 5=2

Interesting! I came up with 26, but, it's an odd use of equal signs, as has been pointed out. Missed the reflexivity solution completely.

As far as the "other solution" goes, I kept looking to the odd language on the original poster image. In fact if we're being quite logical about it, "99% will fail to answer" means that only 1% (presumably of people who see the puzzle) will actually hazard an answer, whether correct or not. It doesn't say that the 99% failed to answer _correctly_, after all.

I also notice that the puzzle starts with the word "if" but there's no "then," or perhaps the "then" is implied. Otherwise a wise guy could say "there's no answer because there's no question!"

All-in-all an interesting mishmash of conventions and assumption-baiting.

Margaret and Fiona

In fact other than 2 and 26 even 24 is a possible answer!! Let me explain it..

2=5 -----> 2+3=5 and 3 is a prime number

3=10----->3+7=10 and 7 is a prime number and observe the pattern of prime numbers added here .. after 3, 5 is not added.

4=17----> 4+13=17 13 is a prime number and in between 7 and 13 , prime number 11 is left.

now, 5=?

5=5+19=24.. leaving prime number 17 in between 13 and 19..

But, answer 2 is more convincing.

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