This is part of our collection of Short Problems.
You may also be interested in our longer problems on Working Systematically.
You may also be interested in our longer problems on Working Systematically.
problem
Grid without lines
Age
11 to 14
Challenge level
Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?
problem
Kept apart
Age
11 to 14
Challenge level
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?
problem
Fruit line-up
Age
11 to 14
Challenge level
This grocer wants to arrange his fruit in a particular order, can you help him?
problem
Colourful tiles
Age
11 to 14
Challenge level
Weekly Problem 21 - 2011
How many ways can you paint this wall with four different colours?
How many ways can you paint this wall with four different colours?
problem
Central sum
Age
11 to 14
Challenge level
Can you find numbers between 100 and 999 that have a middle digit equal to the sum of the other two digits?
problem
Satnav dilemma
Age
11 to 14
Challenge level
How many routes are there in this diagram from S to T?
problem
Negative dice
Age
11 to 14
Challenge level
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?
problem
Magic error
Age
11 to 14
Challenge level
Two of the numbers in a 4x4 magic square have been swapped. Can you work out the sum of these numbers?
problem
Nine, ten and one
Age
11 to 14
Challenge level
Can you find the value of t in these equations?
problem
Subtracting to 2008
Age
11 to 14
Challenge level
Can you work out the sum of the missing digits in this subtraction?
problem
Making 11p
Age
11 to 14
Challenge level
How many ways are there to make 11p using 1p, 2p and 5p coins?
problem
Fly away
Age
11 to 14
Challenge level
Can you work out the values of the digits in this addition sum?
problem
Mini-Sudoku
Age
11 to 14
Challenge level
How many ways are there of completing the mini-sudoku?
problem
Triangular clock
Age
11 to 14
Challenge level
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?
problem
Mini Kakuro
Age
11 to 14
Challenge level
The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?
problem
Isometric rhombuses
Age
11 to 14
Challenge level
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?
The diagram shows a grid of $16$ identical equilateral triangles. How many rhombuses are there made up of two adjacent small triangles?
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
Multiplication table puzzle
Age
11 to 14
Challenge level
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?
problem
Loose change
Age
11 to 14
Challenge level
In how many ways can you give change for a ten pence piece?
problem
Island hopping
Age
11 to 14
Challenge level
What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?
problem
Double with 1 to 9
Age
11 to 14
Challenge level
Can you find a number and its double using the digits $1$ to $9$ only once each?
problem
Rolling along the trail
Age
11 to 14
Challenge level
What could be the scores from five throws of this dice?
problem
The square of my age
Age
11 to 14
Challenge level
Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?
problem
Staircase sum
Age
11 to 14
Challenge level
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?
problem
So many sums
Age
11 to 14
Challenge level
In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?
problem
Blockupied
Age
11 to 14
Challenge level
A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?
problem
Latin multiplication
Age
11 to 14
Challenge level
Can you choose one number from each row and column in this grid to form the largest possibe product?
problem
Middle digit mean
Age
11 to 16
Challenge level
Weekly Problem 16 - 2016
How many three digit numbers have the property that the middle digit is the mean of the other two digits?
How many three digit numbers have the property that the middle digit is the mean of the other two digits?
problem
Even squares
Age
11 to 14
Challenge level
Can you find squares within a number grid whose entries add up to an even total?
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
Kangaroo hops
Age
11 to 14
Challenge level
Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?
Kanga hops ten times in one of four directions. At how many different points can he end up?
problem
Distinct in a line
Age
11 to 14
Challenge level
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?
problem
Adjacent additions
Age
14 to 16
Challenge level
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?
problem
Dicey directions
Age
14 to 16
Challenge level
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?
problem
End of a prime
Age
14 to 16
Challenge level
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?
problem
Threes and fours
Age
14 to 16
Challenge level
What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?
problem
Facial sums
Age
14 to 16
Challenge level
Can you make the numbers around each face of this solid add up to the same total?
problem
No square sums
Age
14 to 16
Challenge level
How many numbers do you need to remove to avoid making a perfect square?
problem
Alberta's age
Age
14 to 16
Challenge level
Alberta won't reveal her age. Can you work it out from these clues?
problem
Alphabetical angle
Age
14 to 16
Challenge level
If all the arrangements of the letters in the word ANGLE are written down in alphabetical order, what position does the word ANGLE occupy?
problem
Relative time
Age
14 to 16
Challenge level
Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?
problem
Gridlines
Age
14 to 16
Challenge level
How many triples of points are there in this 4x4 array that lie on a straight line?
problem
Switch on
Age
14 to 16
Challenge level
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?
problem
Factor list
Age
14 to 16
Challenge level
Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?
problem
Different digital clock
Age
14 to 16
Challenge level
At how many times between 10 and 11 o'clock are all six digits on a digital clock different?
problem
Medal ceremony
Age
14 to 16
Challenge level
The teacher has forgotten which pupil won which medal. In how many different ways could he give the medals out to the pupils?
problem
Phone call
Age
14 to 16
Challenge level
How many different phone numbers are there starting with a 3 and with at most two different digits?
problem
Integer indices
Age
14 to 16
Challenge level
From this sum of powers, can you find the sum of the indices?
problem
Leftovers
Age
14 to 16
Challenge level
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 $n+4$?
If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?