UKMT Cayley Olympiad, 2018

Combinatorics Difficulty 2.0 Junior Prove it United Kingdom

In the puzzle Suko, the numbers from $1$ to $9$ are to be placed in the spaces (one number in each) so that the number in each circle is equal to the sum of the numbers in the four surrounding spaces. How many solutions are there to the Suko puzzle shown alongside? The puzzle is a $3\times3$ grid of spaces with circles at the intersections of the inner $2\times2$ points, labelled (top row) $22$ , $28$ and (bottom row) $11$ , $18$ .

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.