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# Working Systematically - Short Problems

### Making 11p

### Loose Change

### Central Sum

### Mini Kakuro

### Fruit Line-up

### Fly Away

### Mini-sudoku

### Island Hopping

### Satnav Dilemma

### Grid Without Lines

### Negative Dice

### Isometric Rhombuses

### Magic Error

### Colourful Tiles

### Kept Apart

### Half and Half

### Triangular Clock

### Subtracting to 2008

### Multiplication Table Puzzle

### Rolling Along the Trail

### The Square of My Age

### Staircase Sum

### Even Squares

### So Many Sums

### Blockupied

### Latin Multiplication

### Double with 1 to 9

### Kangaroo Hops

### Almost Constant Digits

### Distinct in a Line

### Middle Digit Mean

### Adjacent Additions

### Dicey Directions

### End of a Prime

### Threes and Fours

### Alphabetical Angle

### No Square Sums

### Facial Sums

### Gridlines

### Relative Time

### Alberta's Age

### Switch On

### Factor List

### Phone Call

### Different Digital Clock

### Leftovers

### Medal Ceremony

### Integer Indices

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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.

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

Weekly Problem 21 - 2011

How many ways can you paint this wall with four different colours?

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

Weekly Problem 11 - 2011

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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 $n+4$?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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