Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Natural Sum

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.

Series Sums

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

Charlie's Delightful Machine

Stage: 3 and 4 Challenge Level:

You may wish to look at Shifting Times Tables before trying this problem.

Charlie's Delightful Machine has four coloured lights on it.
You can enter numbers into Charlie's machine.
Each light is controlled by a rule, and if your number satisfies the rule, the light will go on.
Some numbers may turn on more than one light!

Type in some numbers and see which lights you can switch on.
To start again with a new set of rules, click a Level button (each level is more difficult than the last).

Can you develop a strategy to work out the rules controlling each light at Level 1?
Once you have a strategy, challenge yourself to find four digit numbers that turn on each light.

Once you are confident that you can work out the rules for Level 1 lights, try finding rules for some Level 2 and 3 lights.

Alternatively, have a go at A Little Light Thinking, where you can explore how to turn on several lights at once.