Step by step
The question
Question: The pattern Mon, Tue, Wed, Thu, Fri, Mon, Tue, Wed, Thu, Fri, ...
keeps repeating.
What is the 63rd day?
1 Find the block
The list starts again after Fri.
So the block that repeats is Mon, Tue, Wed, Thu, Fri.
block = Mon, Tue, Wed, Thu, Fri
The block is 5 long.
length = 5
2 Divide
The block comes again and again.
So we divide by its length.
What is left over tells us the place in the block.
n ÷ (length of the block): what is left = the place in the block
5 times 12 is 60.
So 12 full blocks take us to the 60th day.
63 minus 60 is 3 more.
63 ÷ 5 = 5 × 12 = 60, 63 − 60 = 3
3 Count into the block
Careful!
The 12 only counts full blocks.
The 3 left over gives the place.
Careful: not 12: the number of blocks ✗
3 left means place 3 in the block: Wed.
63rd day = place 3 in the block = Wed
4 Check
Let's check by counting on.
A block ends at the 60th day.
Then we count on: Mon, Tue, Wed.
The 63rd is Wed.
So it is right!
60th = Fri (end of a block), 61st = Mon, 62nd = Tue, 63rd = Wed ✓
Let's look back.
First: find the block.
Then: divide.
Then: count into the block.
Last: check.
Answer
63rd day = place 3 in the block = Wed