# Working Systematically - Upper Secondary

### Charlie's Delightful Machine

##### Stage: 3 and 4 Challenge Level:

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

### What's Possible?

##### Stage: 4 Challenge Level:

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

### A Long Time at the Till

##### Stage: 4 and 5 Challenge Level:

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

### Sorted

##### Stage: 5 Challenge Level:

How can you quickly sort a suit of cards in order from Ace to King?

##### Stage: 5 Challenge Level:

Can you set the logic gates so that this machine can decide how many bulbs have been switched on?

### Ante Up

##### Stage: 5 Challenge Level:

Use cunning to work out a strategy to win this game.

### Stage 5 Cipher Challenge

##### Stage: 5 Challenge Level:

Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?

### Alphabetical Angle

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 8 - 2014
If all the arrangements of the letters in the word ANGLE are written down in alphabetical order, what position does the word ANGLE occupy?

### Wedding Morning

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 45 - 2015
If Sam is getting married on the 9th of November 2015 aged 30, do you know which year he was born in?

### Fiction in Wonderland

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 17 - 2014
Tweedledum, Tweedledee, Alice and the White Rabbit are having a conversation. How many of the statements they make are true?

### Middle Digit Mean

##### Stage: 3 and 4 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?

### Circle of Lies

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 34 - 2014
Can you work out how many of Pierre, Qadr, Ratna, Sven and Tanya are telling the truth?

### Domino Hexagon

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 18 - 2017
Dominic wants to place the six dominoes above in a hexagonal ring. Which of the dominoes could be placed next to the one shown?

### Mini-sudoku

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 8 - 2015
How many ways are there of completing the mini-sudoku shown?

### No Square Sums

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 12 - 2011
How many numbers do you need to remove to avoid making a perfect square?

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 24 - 2015
In how many ways can you move through the grid to give the digits 2009?

### Phone Call

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 25 - 2015
How many different phone numbers are there starting with a 3 and with at most two different digits?

### Medal Ceremony

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 41 - 2013
The teacher has forgotten which pupil won which medal. In how many different ways could he give the medals out to the pupils?

### Gridlines

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 27 - 2015
How many triples of points are there in this 4x4 array that lie on a straight line?

### Integer Indices

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 6 - 2008
From this sum of powers, can you find the sum of the indices?

### Amazing

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 6 - 2014
A maze has nine rooms, with gaps in the walls between them. How many ways are there to travel from X to Y?

### Switch On

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 39 - 2015
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?