Monster problem

For students of class 6-8 (age 12 to 14)
User avatar
Raiyan Jamil
Posts:138
Joined:Fri Mar 29, 2013 3:49 pm
Monster problem

Unread post by Raiyan Jamil » Sat Feb 08, 2014 12:26 pm

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 ?
A smile is the best way to get through a tough situation, even if it's a fake smile.

User avatar
Thanic Nur Samin
Posts:176
Joined:Sun Dec 01, 2013 11:02 am

Re: Monster problem

Unread post by Thanic Nur Samin » Sat Feb 08, 2014 1:23 pm

The answer is 4 letters
Hammer with tact.

Because destroying everything mindlessly isn't cool enough.

User avatar
Labib
Posts:411
Joined:Thu Dec 09, 2010 10:58 pm
Location:Dhaka, Bangladesh.

Re: Monster problem

Unread post by Labib » Sat Feb 08, 2014 5:53 pm

@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, $K=4$.
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.


"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

Post Reply