14 Divisors

What is the smallest number with exactly 14 divisors?

Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Weekly Problem 42 - 2010

Stage: 3 Short Challenge Level:

If we rewrite the equation we get the product $E\times I\times G \times H\times T = T\times W \times O\times F\times O \times U \times R$.

There are $10$ different letters here, so each number from $0$ to $9$ must be represented by one of the letters. So one letter is $0$. Any product where this letter appears is $0$. Hence both sides must include this letter. The only letter on both sides is $T$.

Hence $T=0$ and the product $T\times H\times R \times E \times E =0$.

This problem is taken from the UKMT Mathematical Challenges.

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