GK 2015 Q17
17. Ria wants to write a number in each of the seven bounded regions in the diagram. Two regions are neighbours if they share part of their boundary. The number in each region is to be the sum of the numbers in all of its neighbours. Ria has already written in two of the numbers, as shown.
What number must she write in the central region?
- A 0
- B 1
- C −2
- D −4
- E 6
Grey Kangaroo 2015, Question 17. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 6
Let the numbers in the four regions that are neighbours to −4 be \(a\), \(b\), \(c\) and \(d\) as shown in the diagram. The question tells us that \(a + b + c + d = -4\). However, we also know that \(a + b + c + d + ? = 2\) and hence \(? = 6\).
(Note: The values \(a = d = -4\) and \(b = c = 2\) give a complete solution to the problem).
Solution © UK Mathematics Trust, from the GK 2015 solutions.