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Mind games and alternative solutions

Wednesday, November 9, 2005 | 2 comments

Last night I browsed a bit through a Scientific American "Mind" edition (volume 16, number 1) I bought some time ago. On page 96 it got some "Head Games" by Abbie F. Salny. I was able to solve one very fast, a pattern completion puzzle.

Figure out the pattern
Figure out the pattern

Today I asked Esme, and later Andreja, a very good online friend, to solve the problem. And no, 64 is not the answer, since it only completes the sequence at the bottom and ignores the other two numbers in each circle.

After some thinking and trying, Andreja came up with a very nice alternative solution. But before explaining that one, lets see what I came up with, and which matches the answer given at the bottom of the page in the Scientific American.

One possible relation between the three numbers
One possible relation between the three numbers

So the number in the bottom of the circle is four times the difference between the left and right number. So the answer could be: 4(12 - 9) = 12. However, Andreja came up with 77. First she added the left and bottom number, see image below:

Alternative solution
Alternative solution

And then by dropping the left most digit on the right number, the same right top sequence is generated, and hence the missing number is 77, since 12 + 77 = 89, and we drop the 8. So the function f in the image below keeps the right most digit of a number:

Another possible relation between the three numbers
Another possible relation between the three numbers

I like this solution, since the digits that are dropped form another sequence: 1, 2, 4, 8. Very good job, and I wonder if more solutions are possible. If you find one, please post a comment.

Andreja is very fond of puzzling games. She beat me big time with the online Alchemy game. And now plays a lot Sudoku online, which I still have to give a serious try.

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