Library / UKMT Grey Kangaroo /199 of 242

UKMT Grey Kangaroo, 2017

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Ella wants to write a number into each cell of a $3 \times 3$ grid so that the sum of the numbers in any two cells that share an edge is the same. She has already written two numbers, as shown in the diagram. When Ella has completed the grid, what will be the sum of all the numbers in the grid?

(A) $18$ (B) $20$ (C) $21$ (D) $22$ (E) $23$

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.