List

Working Systematically - Short Problems

Kept Apart
problem

Kept Apart

Age
11 to 14
Challenge level
filled star empty star empty star
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?
Fruit Line-Up
problem

Fruit Line-Up

Age
11 to 14
Challenge level
filled star empty star empty star
This grocer wants to arrange his fruit in a particular order, can you help him?
Colourful Tiles
problem

Colourful Tiles

Age
11 to 14
Challenge level
filled star empty star empty star
Weekly Problem 21 - 2011
How many ways can you paint this wall with four different colours?
Central Sum
problem

Central Sum

Age
11 to 14
Challenge level
filled star empty star empty star
Can you find numbers between 100 and 999 that have a middle digit equal to the sum of the other two digits?
Satnav Dilemma
problem

Satnav Dilemma

Age
11 to 14
Challenge level
filled star empty star empty star
How many routes are there in this diagram from S to T?
Negative Dice
problem

Negative Dice

Age
11 to 14
Challenge level
filled star empty star empty star
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?
Magic Error
problem

Magic Error

Age
11 to 14
Challenge level
filled star empty star empty star
Two of the numbers in a 4x4 magic square have been swapped. Can you work out the sum of these numbers?
Nine, Ten and One
problem

Nine, Ten and One

Age
11 to 14
Challenge level
filled star empty star empty star
Can you find the value of t in these equations?
Subtracting to 2008
problem

Subtracting to 2008

Age
11 to 14
Challenge level
filled star empty star empty star
Can you work out the sum of the missing digits in this subtraction?
Making 11p
problem

Making 11p

Age
11 to 14
Challenge level
filled star empty star empty star
How many ways are there to make 11p using 1p, 2p and 5p coins?
Fly Away
problem

Fly Away

Age
11 to 14
Challenge level
filled star empty star empty star
Can you work out the values of the digits in this addition sum?
Mini-Sudoku
problem

Mini-Sudoku

Age
11 to 14
Challenge level
filled star empty star empty star
How many ways are there of completing the mini-sudoku?
Flag-tastic
problem

Flag-tastic

Age
11 to 14
Challenge level
filled star empty star empty star
How many different flags can you make?
Triangular Clock
problem

Triangular Clock

Age
11 to 14
Challenge level
filled star empty star empty star
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?
Mini Kakuro
problem

Mini Kakuro

Age
11 to 14
Challenge level
filled star empty star empty star
The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?
Isometric Rhombuses
problem

Isometric Rhombuses

Age
11 to 14
Challenge level
filled star empty star empty star
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?
Half and Half
problem

Half and Half

Age
11 to 14
Challenge level
filled star empty star empty star
Two of the four small triangles are to be painted black. In how many ways can this be done?
Multiplication Table Puzzle
problem

Multiplication Table Puzzle

Age
11 to 14
Challenge level
filled star empty star empty star
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?
Loose Change
problem

Loose Change

Age
11 to 14
Challenge level
filled star empty star empty star
In how many ways can you give change for a ten pence piece?
Island Hopping
problem

Island Hopping

Age
11 to 14
Challenge level
filled star empty star empty star
What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?
Grid without Lines
problem

Grid without Lines

Age
11 to 14
Challenge level
filled star empty star empty star
Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?
Double with 1 to 9
problem

Double with 1 to 9

Age
11 to 14
Challenge level
filled star filled star empty star
Can you find a number and its double using the digits $1$ to $9$ only once each?
Rolling Along the Trail
problem

Rolling Along the Trail

Age
11 to 14
Challenge level
filled star filled star empty star
What could be the scores from five throws of this dice?
The Square of My Age
problem

The Square of My Age

Age
11 to 14
Challenge level
filled star filled star empty star
Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?
Staircase Sum
problem

Staircase Sum

Age
11 to 14
Challenge level
filled star filled star empty star
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?
So Many Sums
problem

So Many Sums

Age
11 to 14
Challenge level
filled star filled star empty star
In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?
Blockupied
problem

Blockupied

Age
11 to 14
Challenge level
filled star filled star empty star
A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?
Latin Multiplication
problem

Latin Multiplication

Age
11 to 14
Challenge level
filled star filled star empty star
Can you choose one number from each row and column in this grid to form the largest possibe product?
Middle Digit Mean
problem

Middle Digit Mean

Age
11 to 16
Challenge level
filled star filled star empty star
Weekly Problem 16 - 2016
How many three digit numbers have the property that the middle digit is the mean of the other two digits?
Even Squares
problem

Even Squares

Age
11 to 14
Challenge level
filled star filled star empty star
Can you find squares within a number grid whose entries add up to an even total?
Almost Constant Digits
problem

Almost Constant Digits

Age
11 to 14
Challenge level
filled star filled star filled star
How many 10-digit numbers containing only 1s, 2s and 3s can you write?
Kangaroo Hops
problem

Kangaroo Hops

Age
11 to 14
Challenge level
filled star filled star filled star
Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?
Distinct in a Line
problem

Distinct in a Line

Age
11 to 14
Challenge level
filled star filled star filled star
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?
Adjacent Additions
problem

Adjacent Additions

Age
14 to 16
Challenge level
filled star empty star empty star
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?
Dicey Directions
problem

Dicey Directions

Age
14 to 16
Challenge level
filled star empty star empty star
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?
End of a Prime
problem

End of a Prime

Age
14 to 16
Challenge level
filled star empty star empty star
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
problem

Threes and Fours

Age
14 to 16
Challenge level
filled star empty star empty star
What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?
No Square Sums
problem

No Square Sums

Age
14 to 16
Challenge level
filled star filled star empty star
How many numbers do you need to remove to avoid making a perfect square?
Alberta's Age
problem

Alberta's Age

Age
14 to 16
Challenge level
filled star filled star empty star
Alberta won't reveal her age. Can you work it out from these clues?
Alphabetical Angle
problem

Alphabetical Angle

Age
14 to 16
Challenge level
filled star filled star empty star
If all the arrangements of the letters in the word ANGLE are written down in alphabetical order, what position does the word ANGLE occupy?
Relative Time
problem

Relative Time

Age
14 to 16
Challenge level
filled star filled star empty star
Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?
Gridlines
problem

Gridlines

Age
14 to 16
Challenge level
filled star filled star empty star
How many triples of points are there in this 4x4 array that lie on a straight line?
Switch On
problem

Switch On

Age
14 to 16
Challenge level
filled star filled star empty star
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?
Facial Sums
problem

Facial Sums

Age
14 to 16
Challenge level
filled star filled star empty star
Can you make the numbers around each face of this solid add up to the same total?
Factor List
problem

Factor List

Age
14 to 16
Challenge level
filled star filled star filled star
Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?
Different Digital Clock
problem

Different Digital Clock

Age
14 to 16
Challenge level
filled star filled star filled star
At how many times between 10 and 11 o'clock are all six digits on a digital clock different?
Medal Ceremony
problem

Medal Ceremony

Age
14 to 16
Challenge level
filled star filled star filled star
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
problem

Phone Call

Age
14 to 16
Challenge level
filled star filled star filled star
How many different phone numbers are there starting with a 3 and with at most two different digits?
Integer Indices
problem

Integer Indices

Age
14 to 16
Challenge level
filled star filled star filled star
From this sum of powers, can you find the sum of the indices?
Leftovers
problem

Leftovers

Age
14 to 16
Challenge level
filled star filled star filled star
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 $n+4$?