Answer to Problem of the Month for December 2022

In each of the Christmas trees below, the number in each hexagon is the sum of the two numbers below it.

Can you fill in all the hexagons with the correct numbers?

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The solution is:

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:

1. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
2. Davit Banana	Istanbul, Turkey
3. K. Sengupta	Calcutta, India
4. Ivy Joseph	Pune, Maharashtra, India
5. Joseph Moore	Denver, Colorado
6. Margot Ganster	Fort Collins, Colorado
7. Ethan Ganster	Fort Collins, Colorado
8. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
9. Brinley Barnes	Mountain View High School, Mountain View, Wyoming
10. Lillian Morwood	Mountain View High School, Mountain View, Wyoming
11. Ritwik Chaudhuri	Santiniketan, West Bengal, India
12. Cody Downey	Mountain View High School, Mountain View, Wyoming
13. Jubilee Ortiz	Central High School, Grand Junction, Colorado
14. Corbin Carey	Central High School, Grand Junction, Colorado
15. Diana and Craig Chastain	Fort Collins, Colorado
16. Tabor	Muckleshoot Tribal School, Auburn, Washington
17. Doreen Elkins	Muckleshoot Tribal School, Auburn, Washington
18. Robert K.	Muckleshoot Tribal School, Auburn, Washington
19. Cameron W.	Muckleshoot Tribal School, Auburn, Washington

December 2022 Problem of the Month

Correctly solved by:

December 2022
Problem of the Month