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Monster problem

Posted: Sat Feb 08, 2014 12:26 pm
by Raiyan Jamil
A four headed monster :evil: :evil: :evil: :evil: has 63 children . He wants to give each child a name of three English letters . And every 63 names will be different . In a name of a child , a letter can be used more than once . What is the minimum number of letters does the monster need to use ?

Re: Monster problem

Posted: Sat Feb 08, 2014 1:23 pm
by Thanic Nur Samin
The answer is 4 letters

Re: Monster problem

Posted: Sat Feb 08, 2014 5:53 pm
by Labib
@Thanic nur Samin, Please practise posting full solutions or at least hints for your solution unless asked explicitly for just the answer to the problem. Because most often, people asking for help are actually asking for ideas/keys to solve the problem and not just the answer.

Here's a possible way to solve this problem.
There are $3$ letters in a name and a letter may appear more than once in a name.
So, if we use $K$ different letters, we can make $K*K*K = K^3$ different names.
According to the problem statement, we want the minimum such $K$ that $ K^3 \geq 63$. So, $K=4$.