### 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...

### Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

### Always the Same

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

# Card Trick 1

##### Age 11 to 14 Challenge Level:

When the pack has been shuffled and then split, let us assume that there are x cards face up in the pile of 20. This being the case, there must be 20 - x cards face up in the second pile. When the pile of 20 is turned upside down there will be 20 - (20 - x) = x cards face up in the pile. Therefore both piles of cards will have the same number of cards ( x ) face up.

Of course the trick works just as well if the volunteer chooses 25 cards or any other number of cards. You might like to convince yourself that this is so by rewriting the above solution replacing 20 by 25.