### 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?

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!

### Rotating Triangle

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

# Weekly Lies

##### Stage: 3 Short Challenge Level:

Mr Ross does not give the same name twice in a row, so the six days cannot include both Thursday and Friday. Therefore day 1 is a Friday or a Saturday.

If day 1 is Saturday, then he says his real name on Thursday (day 6), which is therefore Bob. But he also says Bob on Tuesday (day 4) the day when he definately lies, which is impossible, so day 1 must be a Friday.

In this case his name is John, and day 7 is a Thursday, a day on which he tells the truth. Therefore his answer on the seventh day will also be John.

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution
View the current weekly problem