# A puzzle in kindergarten's book

I found the following puzzle in a kindergarten book:

Can anyone give a clear explanation as to what the answer is and why?

The first time I tried to solve it I got an answer of 6, by noting that the sum of the top and bottom pair of each set are equal:

For the first:

3 6
7
4 5


Where, 3+6 = 4+5

The second:

2 9
9
8 3


2+9 = 8+3

And so on.

But this solution completely ignores the centre number, leading me to believe it is wrong! Can anyone think of a better or more logical solution?

The only logical explanation I can come up with at a kindergarten level of knowledge would be that they author intended the child to spot that the $$\cup$$ and the $$\cap$$ shape have the same sum, i.e. for

3 6
7
4 5


we would have

$$3+7+6=4+7+5$$

As an adult we can very easily spot that we don't need to count the middle one for it to still work however a child may not spot this if they are looking for a pattern which uses all the boxes in each diagram.

This then gives us that

\begin{align}7+5+8&=9+5+?\\ 20&=14+?\\ ?&=6\end{align}

I tried a few other simple patterns, such as summing diagonals, or adding all the numbers and looking for a pattern between the diagrams but nothing jumped out and I think that is getting quite close to the limit of an average kindergarten child's knowledge.

8

because:

add up each set of boxes - 3+6+7+4+5=25, 2+9+9+8+3=31, 7+8+5+9+8=37 for AP(25,6).

Plus:

the typeset gaps between the sets of boxes are wonky, so obviously this kindergarten puzzle is from a low quality text book.

• I think your answer is good enough for kindergarten! Upvoted! – Chau Giang Jan 21 '19 at 3:52

Just a partial answer in all probability:

The missing number is

6

I would be using the following notations for explanation:

Top-Right => TR
Top-Left => TL
Bottom-Right => BR
Bottom-Left => BL


2 reasons:

1.

The sum of the numbers in the upper horizontal boxes is the same as that of the lower ones: TR + TL = BR + BL, hence: 1st: 3 + 6 = 4 + 5; 2nd: 2 + 9 = 8 + 3, which should mean, for the 3rd, 7 + 8 = 9 + BR ==> BR = 6.

2.

The difference between the numbers in the left vertical boxes is the same as that of the right ones: BL - TL = TR - BR, i.e, 1st: 4 -3 = 6 - 5; 2nd: 8 - 2 = 9 - 3, which should mean, for the 3rd: 9 - 7 = 8 - BR ==> BR = 6

P.S

Couldn't figure out what the middle boxes have to do here though.

• Rule 2 is necessarily true if Rule 1 is - rot13(fhogenpg OE naq GY sebz obgu fvqrf) of Rule 1. – ZanyG Jan 17 '19 at 6:55
• good point @Zanyg. I failed to notice that. – Harshith Rai Jan 17 '19 at 8:30
• The middle ones are there to confuse the kids. 4 - 3 = 1 which looks like a seven if written continental European style, 8 -2 = 6 which looks like a 9 if turned upside dow. 9 - 7 = 2 which looks like five if turned upside down :) – yunzen Jan 18 '19 at 11:34