Many Matildas
MatildaMatildaMatil... What is the 1000th letter?
Age
11 to 14
Challenge level
Problem
The name Matilda is written repetitively like this:
$$\text{MatildaMatildaMatilda}......$$What is the $1000$th letter?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $\text d$
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 $\text d$.