Copyright © University of Cambridge. All rights reserved.

## 'Many Matildas' printed from http://nrich.maths.org/

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.*

*View the archive of all weekly problems grouped by curriculum topic*