### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### 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...

# Many Matildas

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

The pattern repeats every seven letters, so the name ends on the $7^\text{th}$, $14^\text{th}$, $21^\text{st}$, ... letters, i.e. on every multiple of $7$.

Since $1000 \div 7 = 142 \text{ r}6$, there are $142$ complete copies of the name, and then the $1000^\text{th}$ letter is the sixth letter of the next name. Therefore the $1000^\text{th}$ letter is $d$.

This problem is taken from the UKMT Mathematical Challenges.