Can you place the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 in the circles below so that the sum
of each row of numbers equals 26?
You get extra credit if the sum of the six vertices of the star also add up to 26.
Solution to the Problem:
There are many solutions to the problem. Here is one where the vertices also add up to 26:
Colin Bowey sent in an xcel spreadsheet that shows 80 unique solutions, each of which can be displayed 12 ways by rotation and reflections, so there are 960 solutions overall.
There are only 6 unique solutions where the vertices = 26, but each of them can be represented 12 ways with rotations and reflections given a total of 72 solutions.
Click here to download his spreadsheet
You may have to click on OPTIONS and ENABLE MACROS in the spreadsheet to get it to run.
Colin gets 72 times the extra credit!
Correctly solved by:
| 1. Kennedy Vis |
Central High School, Grand Junction, Colorado |
| 2. Sidona Johnston |
Central High School, Grand Junction, Colorado |
| 3. Ritwik Chaudhuri ** | Santiniketan, West Bengal, India |
| 4. Veena Mg ** | Bangalore, Karnataka, India |
| 5. Colin (Yowie) Bowey ** | Beechworth, Victoria, Australia |
| 6. Dr. Hari Kishan ** |
D.N. College, Meerut, Uttar Pradesh, India |
| 7. Mya Marquez |
Central High School, Grand Junction, Colorado |
** Extra Credit