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Suit Sequence

Stage: 3 Short Challenge Level: Challenge Level:1
See all short problems arranged by curriculum topic in the short problems collection


A pattern that repeats every six symbols starts as shown below:  $$ \heartsuit \:\: \clubsuit \:\: \heartsuit \:\: \diamondsuit \:\: \heartsuit \:\: \spadesuit \:\: \heartsuit \:\: \clubsuit \:\: \heartsuit \:\: \diamondsuit \:\: \heartsuit \:\: \spadesuit \:\: \ldots$$ What are the $100^{\text{th}}$ and $101^{\text{st}}$ symbols in the pattern?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.