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14 Divisors

What is the smallest number with exactly 14 divisors?

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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?

The Square of My Age

Stage: 3 Short Challenge Level: Challenge Level:1

One method for this question is to notice that the square of Thomas' age is at most $62$, so Thomas is at most $7$. The square of Thomas' age is therefore at most $49$, so Lauren is at least $13$.

The square of Lauren's age is at most $176$, so Lauren is at most $13$. Therefore Lauren must be $13$, and Thomas must be $7$.
 
 

This problem is taken from the UKMT Mathematical Challenges.

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