Odd and even numbers

problem
Make 37

Age

5 to 11

Challenge level

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?
problem
Sets of numbers

Age

7 to 11

Challenge level

How many different sets of numbers with at least four members can you find in the numbers in this box?
problem
What number?

Age

5 to 7

Challenge level

I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.
problem
Diagonal trace

Age

7 to 11

Challenge level

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?
problem
Prime magic

Age

7 to 16

Challenge level

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?
problem
Great Granddad

Age

11 to 14

Challenge level

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?
problem
Comparing continued fractions

Age

16 to 18

Challenge level

Which of these continued fractions is bigger and why?
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?
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.
problem
Grouping goodies

Age

5 to 7

Challenge level

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?