## Friday, January 18, 2013

### A Simple Puzzle

Here is a puzzle that looks simple but I am not sure it is as easy at it seems. Feel free to ask your kids or parents to help you. It is "One age fits all" puzzle.  This puzzle is from a great book of Eye Popping Puzzles by Frank Coussement,Peter De Schepper and Keith Kay.

This stone piles are not random. There is a pattern. Can you figure it out and tell how many stones should be placed where the question mark is?

Your answers accepted any time until midnight on Sunday on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Donnal said...

11

Liz S. said...

11. The middle row is the the top and bottom added together.

Christine Campo said...

11 stones

Sandy said...

11.
In rows, 3rd + 4th = 2nd entry
In columns, bottom + top = middle

SN said...

11 stones should be placed where the question mark is. Each pile in the middle row being the sum of piles in the rows up and down.

Ilya said...

One apparent pattern is the piles in the middle row have the number of stones that is a sum of the neighboring piles above and below. So the missing pile should have 11 stones.

Anonymous said...

The top number in each column added to the bottom number in each column are added to result in the answer in middle column. 5 + 5 = 11.

Gurubandhu

Anonymous said...

That is 6 + 5 = 11.

Gurubandhu

Heidi B. said...

There should be 10 in the pile where the question mark is. Simply add the number of rocks on the top pile to the ones on the bottom pile.

Susan said...

There should be 11 stones at the question mark. In each column, the middle pile is the addition of the top and bottom piles.

Anonymous said...

Not sure what's going on when I try to post on your site (anything to do with the upgrade to Windows 8? who knows?) but here's my answer:

I'm betting there's more than one valid approach, but here's what I'm going with...

The values (meaning number of stones) in the top and bottom rows sum to the number in the middle.

3+1=4

2+2=4

and 4+3=7

So the missing number is 6+5=11

Anonymous said...

The prev answer came from Kim via email.

Tom said...

In each completed column, the difference between the "upper" two piles appears in the "lower" pile.
First column: 4-3=1
Second ...
Third column: 4-2=2
Fourth column: 7-4=3
So I'd say the question mark should be replaced by one stone; 6-1=5
That's one pattern, anyway.

A second pattern is that in each column, the SUM of the bottom and top piles is the number in the middle. If that's the desired answer, then 6+5=11 stones should appear at the mark.

Another pattern (not much of a pattern really), is
#1 column -- 8 stones total
#2 ...
#3 column --8 stones
#4 column -- 14 stones
So perhaps a total of 14 would fit the second column (3 stones there?)

And also, possibly,
There is one pile of one stone
Two piles of two stones
So maybe 3 piles of 3 stones?
But the pattern breaks...
Two piles of 4 stones.
One pile of 5, 6 and 7.

I like the first pattern best, with the "difference" being the key, however the second pattern (sum) is simpler and probably the desired answer.

The middle row is the sum of the top and bottom rows, so the missing number of stones is 6 + 5 = 11.

Jerome said...

The only "pattern" I can see is to put 11 where the ? is.

That way you can subtract the bottom number from the middle number to get the top number.

4 11 4 7
1 5 2 3
=========
3 6 2 4

Any other attempt I make is a variation of that result.

Annie said...

There should be 11 stones. The top row of each column plus the bottom row of each column = the middle row of each column.

anne-marie said...

11. Addition line 1 to line 3.
Happy new year to all.

Anonymous said...

I think there are 11 stones in the missing pile. In each vertical column of stones shown in the picture, the middle pile contains the same number of stones as the top and bottom piles summed together.

TracyZ

tom said...

Tom again, I confused myself a bit the other day and did it the hard way first. I first saw the pattern that the Difference between the two top piles in each column equalled the bottom pile. Then also saw that the Sum of the top and bottom pile (in each column) equalled the middle pile. Same thing, silly me. 13, hope I said.

Jerome's wife said...

I found what I thought was a pattern. I added each row vertically and had a pattern of row one being 8, row 2 is the row in question and I will give you it's value in a moment, row three being 8 and row four being 14. To make it symetrical, which is my pattern, row 2 would have a total value of 14, filling in the question mark with the number 3. So we have 8, 14, 8, 14

Maria said...

Sorry for the late answer unveiling. And thank you very much Jerome for "waking me up" and reminding me. The truth is that spending time with a cute little baby at home is emotionally rewarding but it does wipe out your brain intellectually. And lack of sleep wipes out your memory:)

11 it is!
It seems that almost everyone got it. Great pattern spotting. I couldn't find it for a while myself but you did it fast.
A puzzle point to everyone and welcome to the puzzle playground to all those who are new.

Jerome said...

Since I did this by subtracting rather than adding, you could do it this way. Put a 1 where the question mark is and add another stone in the thousands column of the middle row. That would give you

5147 Now take either one of the two other rows and subtract.

5147
1523
====
3624

Jaci said...

11 :-)

Anonymous said...

I think it's 11 because it is the top and bottom row added together. You just have to be good at math!