Reasoning, convincing and proving

problem
Eleven

Age

11 to 14

Challenge level

Replace each letter with a digit to make this addition correct.
problem
Add 3 dice

Age

7 to 11

Challenge level

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do this?
problem
Football crazy hockey mad

Age

11 to 14

Challenge level

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.
problem
Flight of the Flibbins

Age

11 to 14

Challenge level

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to the new planet?
problem
Pattern of islands

Age

11 to 14

Challenge level

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
problem
Dicing with numbers

Age

11 to 14

Challenge level

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?
problem
Not necessarily in that order

Age

11 to 14

Challenge level

Baker, Cooper, Jones and Smith are four people whose occupations are teacher, welder, mechanic and programmer, but not necessarily in that order. What is each person’s occupation?
problem
Master minding

Age

11 to 14

Challenge level

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?
problem
Marbles in a box

Age

11 to 16

Challenge level

How many winning lines can you make in a three-dimensional version of noughts and crosses?
problem
Number rules - OK

Age

14 to 16

Challenge level

Can you produce convincing arguments that a selection of statements about numbers are true?