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
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?
problem
Fruit Line-Up
This grocer wants to arrange his fruit in a particular order, can you help him?
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Colourful Tiles
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
Can you find numbers between 100 and 999 that have a middle digit equal to the sum of the other two digits?
problem
Negative Dice
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?
problem
Magic Error
Two of the numbers in a 4x4 magic square have been swapped. Can you work out the sum of these numbers?
problem
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?
problem
Mini Kakuro
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
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
Two of the four small triangles are to be painted black. In how many ways can this be done?
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Multiplication Table Puzzle
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
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?
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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?
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Double with 1 to 9
Can you find a number and its double using the digits $1$ to $9$ only once each?
problem
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?
problem
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?
problem
So Many Sums
In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?
problem
Blockupied
A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?
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Latin Multiplication
Can you choose one number from each row and column in this grid to form the largest possibe product?
problem
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?
How many three digit numbers have the property that the middle digit is the mean of the other two digits?
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Even Squares
Can you find squares within a number grid whose entries add up to an even total?
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Almost Constant Digits
How many 10-digit numbers containing only 1s, 2s and 3s can you write?
problem
Kangaroo Hops
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
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
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
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
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?
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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?
problem
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?
problem
Relative Time
Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?
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Gridlines
How many triples of points are there in this 4x4 array that lie on a straight line?
problem
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?
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Facial Sums
Can you make the numbers around each face of this solid add up to the same total?
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Factor List
Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?
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Different Digital Clock
At how many times between 10 and 11 o'clock are all six digits on a digital clock different?
problem
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?
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Phone Call
How many different phone numbers are there starting with a 3 and with at most two different digits?
problem
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 $n+4$?
If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?