Working Systematically - Short Problems
Mini-sudoku
How many ways are there of completing the mini-sudoku?
Colourful Tiles
Weekly Problem 21 - 2011
How many ways can you paint this wall with four different colours?
Kept Apart
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?
Triangular Clock
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?
Isometric Rhombuses
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?
Making 11p
How many ways are there to make 11p using 1p, 2p and 5p coins?
Loose Change
In how many ways can you give change for a ten pence piece?
Central Sum
Can you find numbers between 100 and 999 that have a middle digit equal to the sum of the other two digits?
Mini Kakuro
The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?
Half and Half
Two of the four small triangles are to be painted black. In how many ways can this be done?
Fruit Line-up
This grocer wants to arrange his fruit in a particular order, can you help him?
Fly Away
Can you work out the values of the digits in this addition sum?
Island Hopping
What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?
Satnav Dilemma
How many routes are there in this diagram from S to T?
Grid Without Lines
Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?
Negative Dice
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?
Even Squares
Can you find squares within a number grid whose entries add up to an even total?
So Many Sums
In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?
Blockupied
A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?
Staircase Sum
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?
Double with 1 to 9
Can you find a number and its double using the digits $1$ to $9$ only once each?
Rolling Along the Trail
What could be the scores from five throws of this dice?
Latin Multiplication
Can you choose one number from each row and column in this grid to form the largest possibe product?
The Square of My Age
Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?
Almost Constant Digits
How many 10-digit numbers containing only 1s, 2s and 3s can you write?
Distinct in a Line
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?
Kangaroo Hops
Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?
Middle Digit Mean
Weekly Problem 16 - 2016
How many three digit numbers have the property that the middle digit is the mean of the other two digits?
End of a Prime
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?
Threes and Fours
What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?
Dicey Directions
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?
No Square Sums
How many numbers do you need to remove to avoid making a perfect square?
Facial Sums
Can you make the numbers around each face of this solid add up to the same total?
Alberta's Age
Alberta won't reveal her age. Can you work it out from these clues?
Gridlines
How many triples of points are there in this 4x4 array that lie on a straight line?
Switch On
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?
Alphabetical Angle
If all the arrangements of the letters in the word ANGLE are written down in alphabetical order, what position does the word ANGLE occupy?
Different Digital Clock
At how many times between 10 and 11 o'clock are all six digits on a digital clock different?
Leftovers
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 $n+4$?
Medal Ceremony
The teacher has forgotten which pupil won which medal. In how many different ways could he give the medals out to the pupils?
Phone Call
How many different phone numbers are there starting with a 3 and with at most two different digits?
Integer Indices
From this sum of powers, can you find the sum of the indices?
Factor List
Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?