# 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.

### 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?

### 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?

### 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?