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?

Dozens

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Expanding Pattern

Stage: 3 Short Challenge Level:

One way to proceed is to regard the pattern as four arms, each two squares wide, with four corner pieces of three squares each. So for the $n^\text{th}$ pattern, we have $4 \times 2 \times n + 4 \times 3 = 8n +12$. For $n=10$, we need $8 \times 10 +12$, i.e. $92$ squares.

This problem is taken from the UKMT Mathematical Challenges.

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