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Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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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?

Alberta's Age

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Since half of her age is an integer, the second digit of Alberta's age must be even. When the digits are swapped, this is less than half of her age, so the second digit must be one of $0$, $2$ or $4$.

Adding $1$ to the first digit and doubling must produce the same final digit as the second digit, since this determines the final digit when the digits are swapped, 1 is added and then the result doubled. This leads to the following combinations:

Second Digit First Digit
$0$ $4$ or $9$
$2$ $0$ or $5$
$4$ $1$ or $6$

The only combination of these that works is $52$, so Alberta is $52$.

This problem is taken from the UKMT Mathematical Challenges.
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