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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?

Alien Currency

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Let the value of a green note and the value of a blue note be $g$ zogs and $b$ zogs respectively. Then $3g + 8b = 46$ and $8g + 3b = 31$. Adding these two equations gives $11g + 11b = 77$, so $b + g = 7$.

Therefore $3g + 3b = 21$. Subtracting this equation from the original equations in turn gives $5b = 25$ and $5g = 10$ respectively. So $b = 5$, $g = 2$ and $2g + 3b = 19$.

This problem is taken from the UKMT Mathematical Challenges.
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