The block of six symbols $\heartsuit \:\: \clubsuit \:\: \heartsuit \:\: \diamondsuit \:\: \heartsuit \:\: \spadesuit$ repeats every six symbols. $100 \div 6 = 16 \text{ r }4$. This means a block will end on the $96^\text{th}$ symbol, so a new one will start on the $97^\text{th}$. The $100^\text{th}$ symbol will therefore be the same as the $4^\text{th}$ and the $101^\text{st}$ will be the same as the $5^\text{th}$.

Therefore these will be $\diamondsuit \:\: \heartsuit$.

This problem is taken from the UKMT Mathematical Challenges.

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