Counting

problem
Slippery snail

Age

7 to 16

Challenge level

A game for two people, who take turns to move the counters. The player to remove the last counter from the board wins.
problem
Nim-7

Age

5 to 11

Challenge level

Can you work out how to win this game of Nim? Does it matter if you go first or second?
problem
Back to the planet of Vuvv

Age

11 to 14

Challenge level

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. Can you work out in which direction the Zios and Zepts were looking, based on the information you're given?
problem
Find a path

Age

5 to 7

Challenge level

Can you find a path from a number at the top of this network to the bottom which goes through each number from 1 to 9 once and once only?
problem
Spelling circle

Age

7 to 11

Challenge level

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
problem
Mrs Beeswax

Age

5 to 7

Challenge level

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
problem
Page numbers

Age

7 to 11

Challenge level

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
problem
Euromaths

Age

11 to 14

Challenge level

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?
problem
Pairs

Age

11 to 14

Challenge level

Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was thinking of.
problem
Neighbours

Age

7 to 11

Challenge level

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?