Product and sum
When Jim rolled some dice, the scores had the same product and sum. How many dice did Jim roll?
Age
11 to 14
Challenge level
Problem
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?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Let the number of scores of $1$ be $n$. Then the product of the scores is $1^n\times 2\times 3\times 5 =30$. Therefore $1\times n +2 + 3+ 5 = 30$, i.e. $n=20$. So Jim threw $23$ dice.