23. A total of 2021 coloured koalas are arranged in a row and are numbered from 1 to 2021. Each koala is coloured red, white or blue. Amongst any three consecutive koalas, there are always koalas of all three colours. Sheila guesses the colours of five koalas. These are her guesses: Koala 2 is white; Koala 20 is blue; Koala 202 is red; Koala 1002 is blue; Koala 2021 is white. Only one of her guesses is wrong. What is the number of the koala whose colour she guessed incorrectly?
A 2
B 20
C 202
D 1002
E 2021
SolUtion
B

Since the question tells us that amongst any three consecutively numbered koalas, there are always koalas of all three colours, the colours of the koalas will repeat every three koalas. The numbers of the koalas we have information about are $2,20=6 \times 3+2,202=67 \times 3+1$, $1002=334 \times 3$ and $2021=673 \times 3+2$. It can be seen that 2,20 and 2021 all give the same remainder when divided by 3 and hence, since the colours repeat every three koalas, these koalas should be the same colour. However, koala 20 is guessed to be blue, whereas koalas 2 and 2021 are both guessed to be white, so it is koala 20 whose colour has been guessed incorrectly.