### 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?

### Paving Paths

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

# Odds, Evens and More Evens

##### Age 11 to 14Challenge Level

For Alison's approach:

What happens to the numbers as you go down the rows?
What happens as you go up the rows?

For Bernard's approach:

Which numbers end in a 0 in row $A_2$?
Which numbers end in a 0 in row $A_3$?
Which of these sequences will hit 1000?

For Charlie's approach:

Can you find a similar method to Charlie's to describe the other rows?
Which descriptions include 1000?