This group of tasks forms part of our Generalising and Proof Feature and will help push you a bit further into proof after 'limbering up'. In each task, you are challenged to find a general rule.

problem
Nim-7
Can you work out how to win this game of Nim? Does it matter if you go first or second?

problem
Magic Vs
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

problem
Three dice
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

problem
Play to 37
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

problem
Got it
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

problem
Button-up some more
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
