Christmas Problem

Logic Level 3

On the tree above, 4 circles lie on each side of the two big triangles. Place all the numbers 1 to 16 in the circles (some are already placed) so that the 4 numbers on any side add up to 34. Then what is the number which comes in the top most circle?

13 4 9 7 15 2

Anish Harsha by Anish Harsha , 20, India

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2 solutions

Anish Harsha
Dec 25, 2015

Here would be the answer

The number in top most circle is 7.

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Can you show how the answer must be 7?

Pi Han Goh - 5 years, 5 months ago

I SOLVED IT THE SAME WAY

Ashish Menon - 5 years, 5 months ago
Kostis Smanis
Jan 14, 2016

Here's a tip. Let's have it with coordinates so that (1,1) is the top circle, (2,1)=1 and (2,2)=9 and so on. Since 34 is even then we can say that 14+1=15 which is odd. So from (1,1) and (3,1) one must be even and one must be odd. Again, since 16 is even from (1,1),(2,2) and (4,4) all must be even or 2 must be odd and one even. If you continue with this ''strategy'' while having in mind which numbers you can input (7,9,13,15,2,4,8,10,14), I believe it will be easier placing them rather than trial and error. That's all!

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