How many Children?

Number Theory Level pending

A packet has less that $100$ chocolates which when equally distributed to $7,8~\text{or}~9$ children $2,5~\text{and}~3$ chocolates are left out. What should be the maximum number of children so that the chocolates can be equally distributed among them with no chocolates left out and each of them will get more than $\text{one}$ chocolate?

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The answer is 31.

1 solution

Department 8
May 27, 2018

Let total no. Of chocolate be $k$ . This value when subtracted by $2, 5, 3$ is divisible by $7, 8, 9$ respectively. In order to find maximum number of children the number of chocolate should be close to 100. Also $k -3$ is divisible by 9 so it can be 90 or 99, so $\boxed{k = 93 = 31 \times 3}$ . Max number of children is 31.

How many Children?

The answer is 31.

1 solution

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