Working Systematically - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Working Systematically.

Satnav Dilemma

Age 11 to 14 Short Challenge Level:

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

Negative Dice

Age 11 to 14 Short Challenge Level:

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

Half and Half

Age 11 to 14 Short Challenge Level:

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

Loose Change

Age 11 to 14 Short Challenge Level:

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

Nine, Ten and One

Age 11 to 14 Short Challenge Level:

Can you find the value of t in these equations?

Grid Without Lines

Age 11 to 14 Short 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?

Mini-sudoku

Age 11 to 14 Short Challenge Level:

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

Making 11p

Age 11 to 14 Short Challenge Level:

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

Central Sum

Age 11 to 14 Short Challenge Level:

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

Colourful Tiles

Age 11 to 14 Short Challenge Level:

Weekly Problem 21 - 2011
How many ways can you paint this wall with four different colours?

Isometric Rhombuses

Age 11 to 14 Short 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?

Flag-tastic

Age 11 to 14 Short Challenge Level:

How many different flags can you make?

Double with 1 to 9

Age 11 to 14 Short Challenge Level:

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

Even Squares

Age 11 to 14 Short Challenge Level:

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

Latin Multiplication

Age 11 to 14 Short Challenge Level:

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

Rolling Along the Trail

Age 11 to 14 Short Challenge Level:

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

Staircase Sum

Age 11 to 14 Short 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?

Middle Digit Mean

Age 11 to 16 Short 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?

Threes and Fours

Age 14 to 16 Short 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?

End of a Prime

Age 14 to 16 Short 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?

Alberta's Age

Age 14 to 16 Short Challenge Level:

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

Gridlines

Age 14 to 16 Short Challenge Level:

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

Switch On

Age 14 to 16 Short 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?

Alphabetical Angle

Age 14 to 16 Short 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?

No Square Sums

Age 14 to 16 Short Challenge Level:

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

Phone Call

Age 14 to 16 Short Challenge Level:

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

Integer Indices

Age 14 to 16 Short Challenge Level:

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

Different Digital Clock

Age 14 to 16 Short Challenge Level:

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

Medal Ceremony

Age 14 to 16 Short 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?