PK 2016 Q6
6. Marie changed her dice by replacing 1, 3, and 5 with −1, −3 and −5 respectively. She left the even numbers unchanged. If she throws two such dice, which of the following totals cannot be achieved?
- A 3
- B 4
- C 5
- D 7
- E 8
Pink Kangaroo 2016, Question 6. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 7
Any odd score must be the sum of an even (positive) number and an odd (negative number). The largest odd total will be the largest even number added to the smallest odd number, which is 6 + −1 = 5. Hence Marie cannot achieve 7. The others are achievable: 3 = 4 + −1; 4 = 2 + 2; 5 = 6 + −1; 8 = 4 + 4.
Solution © UK Mathematics Trust, from the PK 2016 solutions.