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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?

Takeaway Time

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

Since all the students who liked pizza also liked Chinese, and no student liked all three, we can just think about the remaining $25$ students.

Of these, $14$ liked Chinese and $16$ liked Indian. Since each student liked at least one of these, and there are a total of $30$ 'likes', $5$ students must like both Indian and Chinese.

This leaves $11$ students who liked Indian only.
 
 

This problem is taken from the UKMT Mathematical Challenges.

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