Many Matildas

Age 11 to 14

ShortChallenge Level Yellow star

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

$\text d$ .

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

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