Odd and even numbers

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Favourite

Odds and Evens

Age

11 to 14

Challenge level

Are these games fair? How can you tell?
problem
Favourite

Odds, Evens and More Evens

Age

11 to 14

Challenge level

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
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Favourite

Magic Letters

Age

11 to 14

Challenge level

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
problem

Summats Clear

Age

16 to 18

Challenge level

Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.
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Arrangements

Age

7 to 11

Challenge level

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
problem

Score

Age

11 to 14

Challenge level

There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about a total of 15 with 6 odd numbers?
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Comparing Continued Fractions

Age

16 to 18

Challenge level

Which of these continued fractions is bigger and why?
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Jenny's Logic

Age

11 to 14

Challenge level

Weekly Problem 52 - 2009
How did Jenny figure out that Tom's cards added to an even number?
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Next-Door Numbers

Age

5 to 7

Challenge level

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
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The Set of Numbers

Age

5 to 7

Challenge level

Can you place the numbers from 1 to 10 in the grid?