This puzzle uses 17 Russian coins:
Five 20 kopek coins
Three 15 kopek coins
Three 10 kopek coins
Six 5 kopek coins
Place a coin in each square of the diagram so that the number of kopeks along each straight line is 55.
Solution to the Problem:
There are many solutions. Here are two of them:
James alarie sent in his excellent analysis of the problem:
The only way to have three coins add to 55 is by using two 20's and a 15.
You need a 15 for each of the four sides but only have three 15's, so one of them must be in a corner.
Four of the 20's are used up on the two sides adjoining that corner 15, so you only have one left for the other two sides. It must be in the corner diagonally opposite that corner 15.
The two remaining 15's have to go in the empty slots on the sides.
The diagonal already having 20's at it's end points needs three coins to fill it's slots. The only way to do that is with three 5's.
That leaves six empty slots for the three 10's and remaining three 5's. There are eight ways of putting them in to add to 55 as needed, but two of those are reflections of others.
There are six unique solutions not counting rotations and reflections.
Counting rotations and reflections, there are thirty-two solutions.
One corner must be a 15 coin and it can be any one of the four rotational positions.
Once that 15-corner is set, the remainder of the outer ring is set and does not change through rotation nor reflection.
The (20,5,5,5,20) diagonal is forced.
There are eight ways of placing the remaining coins to satisfy the 55-total rule. This eight accounts for all rotations and reflections.
Eight times four is thirty-two.
Correctly solved by:
| 1. Soonho You | JeonJu, South Korea |
| 2. James Alarie | Flint, Michigan |
| 3. Ivy Joseph | Pune, Maharashtra, India |
| 4. Alyxa Martin |
Mountain View High School, Mountain View, Wyoming |
| 5. Kendall Carr |
Mountain View High School, Mountain View, Wyoming |
| 6. Aubree Andre |
Delta High School, Delta, Colorado |
| 7. Gauge Lockhart |
Delta High School, Delta, Colorado |
| 8. Katelynn Hope |
Mountain View High School, Mountain View, Wyoming |
| 9. Cortlin Condos |
Mountain View High School, Mountain View, Wyoming |
| 10. Skyler Kraai |
Delta High School, Delta, Colorado |
| 11. Kenzy Kellum |
Mountain View High School, Mountain View, Wyoming |
| 12. Adam Bates |
Mountain View High School, Mountain View, Wyoming |
| 13. Breckin Barnes |
Mountain View High School, Mountain View, Wyoming |
| 14. Izabell Hickey |
Mountain View High School, Mountain View, Wyoming |
| 15. Braeden Walk |
Mountain View High School, Mountain View, Wyoming |
| 16. Aubrey Reger |
Mountain View High School, Mountain View, Wyoming |
| 17. Martin Corral |
Delta High School, Delta, Colorado |
| 18. Scott Wells |
Delta High School, Delta, Colorado |
| 19. Tara L. Fiedler |
Goose Creek CISD, Baytown, Texas |
| 20. Figen Furtun | Istanbul, Turkey |
| 21. Brijesh Dave | Mumbai City, Maharashtra, India |
| 22. Kelly Stubblefield | Mobile, Alabama |