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Pairs of numbers

5 to 7
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If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Six Ten Total
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Six ten total

7 to 11
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This challenge combines addition, multiplication, perseverance and even proof.

Consecutive Numbers
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Consecutive numbers

7 to 14
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An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

m, m and m
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M, M and M

11 to 14
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If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Inclusion Exclusion
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Inclusion exclusion

11 to 14
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How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
Mechanical Integration
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Mechanical integration

16 to 18
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To find the integral of a polynomial, evaluate it at some special points and add multiples of these values.
Three by Three
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Three by three

5 to 11
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Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
Gold Again
problem

Gold again

16 to 18
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Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.
Ten Green Bottles
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Ten green bottles

7 to 11
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Do you know the rhyme about ten green bottles hanging on a wall? If the first bottle fell at ten past five and the others fell down at 5 minute intervals, what time would the last bottle fall down?
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