In each tree below, each of the fifteen hexagons has a numerical value that is a positive integer.
Each hexagon is the sum of the two hexagons directly below it, and no two hexagons in any given puzzle have the same value.
You have been given the value of the top hexagon in each puzzle.
Can you find the values of all of the hexagons?
Click here for a printer version
Solution to the Problem:
Click here for Dr. Kishan's thought process in solving this problem.
Here is Davit Banana's explanation of how he used Excel to help solve the problem:
First I assumed that all of the bottom line numbers have to be less than 10.
Then I listed all the combinations by Excel.
When the "sum rules" are applied to fourth, third, second and first (top) lines, you can see and eliminate the top numbers of 43 / 44 / 45 sets.
Just to check that all numbers are different, it takes 4-5 minutes to find.
Colin Bowey gets extra credit for recognizing that there are two answers for each tree (by reversing the numbers in each row)
Click here to see both answers for each tree
Ievgen Murzak also receives extra credit for finding both answers for each tree using a computer program.
Click here for Ievgen Murzak's explanation
Click here to see his code
Correctly solved by:
| 1. Dr. Hari Kishan |
D.N. College, Meerut, Uttar Pradesh, India |
| 2. Ivy Joseph | Pune, Maharashtra, India |
| 3. Davit Banana | Istanbul, Turkey |
| 4. Rob Miles | Northbrook, Illinois, USA |
| 5. Kamal Lohia | Hisar, Haryana, India |
| 6. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
| 7. Ievgen Murzak | Kyiv, Ukraine |
| 8. Kelly Stubblefield | Mobile, Alabama, USA |