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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?

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

Central Sum

Stage: 3 Short Challenge Level: Challenge Level:1

Consider numbers whose fist digit is 1. Looking at each possible value for the second digit we find 9 such numbers.

110, 121, 132, 143, 154, 165, 176, 187, 198.

Similarly there are 8 numbers starting with 2; 7 numbers starting with 3...

Lastly there is only one number starting with 9: 990.

Hence the total is 9+8+7+6+5+4+3+2+1 = 45.

This problem is taken from the UKMT Mathematical Challenges.

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