December 2022 Problem of the Month

Sum Christmas Trees

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Solution to the Problem:

         

         

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Here is an explanation:

In the first tree, let w represent the number in the bottom row, 3rd hexagon over.
Let y and x represent the numbers in the hexagons above w.
Then you can set up three equations with the three unknowns:
5 + w = y
9 + w = x
x + y = 20

         
So, 5 + (x - 9) = y
x - y = 4
x + y = 20
2x = 24
x = 12
Then y = 8 and w = 3.
All the rest of the numbers can be obtained by adding or subtracting various cells.

In the second tree, let a and b represent the numbers in the middle two hexagons in the second from the bottom row.

         
Then the three cells just above a and b would be represented by (17 + a), (a + b) and (b + 10).
You can then write two equations:
(a + b) + (b + 10) = 37 and
(17 + a) + (a + b) = 50

Then solving these equations gives you b = 7 and a = 13.
All the rest of the numbers can be obtained by adding or subtracting various cells.

Correctly solved by: