IMC 2013 Q8
8. Jim rolled some dice and was surprised that the sum of the scores on the dice was equal to the product of the scores on the dice. One of the dice showed a score of 2, one showed 3 and one showed 5. The rest showed a score of 1. How many dice did Jim roll?
- A 10
- B 13
- C 17
- D 23
- E 30
Intermediate Mathematical Challenge 2013, Question 8. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 23
Let the number of scores of 1 be \(n\). Then the product of the scores is 1\(n\) × 2 × 3 × 5 = 30. Therefore 1 × \(n\) + 2 + 3 + 5 = 30, i.e. \(n\) = 20. So Jim threw 23 dice.
Solution © UK Mathematics Trust, from the IMC 2013 solutions. Longer versions with investigations: Solutions and investigations (PDF).