Odd and even numbers

There are 70 NRICH Mathematical resources connected to Odd and even numbers
Make 37 Poster
problem

Make 37

Age
7 to 11
Challenge level
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Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

Sets of Numbers
problem

Sets of Numbers

Age
7 to 11
Challenge level
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How many different sets of numbers with at least four members can you find in the numbers in this box?
What number?
problem

What number?

Age
5 to 7
Challenge level
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I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.
Diagonal Trace
problem

Diagonal Trace

Age
7 to 11
Challenge level
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You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?
Prime Magic
problem

Prime Magic

Age
7 to 16
Challenge level
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Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
Great Granddad
problem

Great Granddad

Age
11 to 14
Challenge level
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Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
Score
problem

Score

Age
11 to 14
Challenge level
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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?
Summats Clear
problem

Summats Clear

Age
16 to 18
Challenge level
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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.
Grouping Goodies
problem

Grouping Goodies

Age
5 to 7
Challenge level
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Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?