Yeaterday I picked up my free copy of The Times with my My Waitrose Card and on page 3 it had this puzzle:
- You must place the numbers 1-9 in the 9 squares, using each number only once.
- The number in each circle should be equal to the sum of the four surrounding squares.
- Each colour sum is correct.
This puzzle turns out to be trickier than it looks, and this was the intention according to this little bit of history. The puzzle was created by Jai Gomer of Kobayaashi Studios.
The three pictures below show my workings to solve this puzzle.
To start with we have 9 unknowns and 7 equations so clearly an indeterminate system; hence brute mathematical force alone won’t be sufficient. Applying a bit of logic we can deduce two of the numbers. At this point I thought great, now I have 7 unknowns but 7 equations. However this was very foolish of me, as in fact we only really have 5 equations for our remaining 7 unknowns. And so, I had to make a few educated guesses on the likely magnitudes of some of the unknowns based on the totals that they contributed to. Once I had done this, the other unknowns dropped out fairly easily and a quick verification at the end showed that I had all the values correct. It could have been different though if I had been incorrect with these educated guesses.
So I have a few unanswered questions
- Have I missed something? Could I have done it without these educated guesses?
- Could I remove one condition and the solution still be unique?
- Would colour totals split into 3,3,3 squares instead of 2,3,4 lead to easier or harder puzzles?
I shall ponder these….