This is part of our collection of Short Problems.
You may also be interested in our longer problems on Probability - Stage 3.
Printable worksheets containing selections of these problems are available here
problem
Satnav dilemma
Age
11 to 14
Challenge level
How many routes are there in this diagram from S to T?
problem
Birthday party
Age
11 to 14
Challenge level
The 30 students in a class have 25 different birthdays between them. What is the largest number that can share any birthday?
problem
Would you like a jelly baby?
Age
11 to 14
Challenge level
What is the smallest number of jelly babies Tom must take, to be certain that he gets at least one of each flavour?
problem
Half and half
Age
11 to 14
Challenge level
Two of the four small triangles are to be painted black. In how many ways can this be done?
problem
Strange dice
Age
11 to 14
Challenge level
If two of these unusually numbered dice are thrown, how many different sums are possible?
problem
School dinners
Age
11 to 14
Challenge level
Our school dinners offer the same choice each day, and each day I try a new option. How long will it be before I eat the same meal again?
problem
Monkey puzzle
Age
11 to 14
Challenge level
What is the probability that all three monkeys left the cafe wearing the wrong hats?
problem
Pieces of eight
Age
11 to 14
Challenge level
Two of the triangles in the diagram are shaded black. What is the probability the resulting figure has at least one line of symmetry?
problem
Clubs
Age
11 to 14
Challenge level
How many students are in the maths club and the science club?
problem
Nine or ten?
Age
11 to 14
Challenge level
Is a score of 9 more likely than a score of 10 when you roll three dice?
problem
Almost constant digits
Age
11 to 14
Challenge level
How many 10-digit numbers containing only 1s, 2s and 3s can you write?
problem
Counting socks
Age
11 to 14
Challenge level
Can you work out the smallest number of socks Rachel needs to take out of the box to be guaranteed a pair?
problem
Perfect score
Age
11 to 14
Challenge level
Can you work out how many children answered all the questions correctly?
problem
Fair's fair
Age
11 to 14
Challenge level
Can you design a die which rolls 'fairly' against mine?