Working Systematically - Short Problems

The squares of this grid contain one of the letters P, Q, R and S. Can you complete this square so that touching squares do not contain the same letter? How many possibilities are there?

This grocer wants to arrange his fruit in a particular order, can you help him?

Weekly Problem 21 - 2011
How many ways can you paint this wall with four different colours?

Can you find numbers between 100 and 999 that have a middle digit equal to the sum of the other two digits?

How many routes are there in this diagram from S to T?

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

Two of the numbers in a 4x4 magic square have been swapped. Can you work out the sum of these numbers?

Can you find the value of t in these equations?

Can you work out the sum of the missing digits in this subtraction?

How many ways are there to make 11p using 1p, 2p and 5p coins?

Can you work out the values of the digits in this addition sum?

How many ways are there of completing the mini-sudoku?

How many different flags can you make?

Trinni rearanges numbers on a clock face so each adjacent pair add up to a triangle number... What number did she put where 6 would usually be?

The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?

Weekly Problem 31 - 2016
The diagram shows a grid of $16$ identical equilateral triangles. How many rhombuses are there made up of two adjacent small triangles?

Can you solve this magic square?

Two of the four small triangles are to be painted black. In how many ways can this be done?

In the multiplication table on the right, only some of the numbers have been given. What is the value of A+B+C+D+E?

In how many ways can you give change for a ten pence piece?

What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?

Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?

Can you find a number and its double using the digits $1$ to $9$ only once each?

What could be the scores from five throws of this dice?

Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?

The digits 1-9 have been written in the squares so that each row and column sums to 13. What is the value of n?

In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?

A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?

Can you choose one number from each row and column in this grid to form the largest possibe product?

Weekly Problem 16 - 2016
How many three digit numbers have the property that the middle digit is the mean of the other two digits?

Can you find squares within a number grid whose entries add up to an even total?

How many 10-digit numbers containing only 1s, 2s and 3s can you write?

Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?

This grid can be filled so that each of the numbers 1, 2, 3, 4, 5 appears just once in each row, column and diagonal. Which number goes in the centre square?

In a 7-digit numerical code, each group of four consecutive digits adds to 16, and each group of five consecutive digits adds to 19. What is the sum of all 7 digits?

An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?

I made a list of every number that is the units digit of at least one prime number. How many digits appear in the list?

What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?

How many numbers do you need to remove to avoid making a perfect square?

Alberta won't reveal her age. Can you work it out from these clues?

If all the arrangements of the letters in the word ANGLE are written down in alphabetical order, what position does the word ANGLE occupy?

Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?

How many triples of points are there in this 4x4 array that lie on a straight line?

In how many different ways can a row of five "on/off" switches be set so that no two adjacent switches are in the "off" position?

Can you make the numbers around each face of this solid add up to the same total?

Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?

At how many times between 10 and 11 o'clock are all six digits on a digital clock different?

The teacher has forgotten which pupil won which medal. In how many different ways could he give the medals out to the pupils?

How many different phone numbers are there starting with a 3 and with at most two different digits?

From this sum of powers, can you find the sum of the indices?

Weekly Problem 26 - 2008
If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?