You may also like

problem icon

Calendar Capers

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of your choice from the second row. You should now have just one number left on the bottom row, circle it. Find the total for the three numbers circled. Compare this total with the number in the centre of the square. What do you find? Can you explain why this happens?

problem icon

Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

problem icon

Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

One O Five

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100 but not to tell you which number they have in mind. Then ask them to tell you the remainders when this number is divided by 3, when it is divided by 5 and when it is divided by 7. Now multiply the first remainder by 70, the second remainder by 21 and the third remainder by 15 and add the three answers together. Now subtract multiples of 105 from this total to give as small a positive whole number as possible. This will be the number your friend first thought of. Test this out a few times and explain why it works.