As a kid, I used to hear stories of child prodigies being able to figure out what day of the week it is say 1000 days from today. In fact, what is it?

Apart from that, let’s try and tackle today’s puzzle about the day of the week of the 100th day of the year N – 1.

Oh and by the way, I finally purchased the premium Canva subscription, let’s hope we will solve more fun and aesthetically pleasing puzzles together!

You know what they say? What is beautiful is good.

Anyway I encourage you to give this problem a go, and when you are ready, keep reading for the solution.

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Solution

So we are told that the 300th day of year N is Tuesday and that the 200th day of year N + 1 is also Tuesday.

Depending on whether year N is a leap year, we have the following as the number of days between the two dates.

The first case is when year N is not leap; the second case is when it is.

7 divides into 266 but not 265. Here this means there are exactly 38 weeks between the 300th day of year N and the 200th day of year N + 1.

In order for both days to be a Tuesday, year N must be a leap year.

Well if year N is a leap year, year N – 1 is NOT a leap year.

Let’s find how many days separate the 100th day of year N − 1 and the 300th day of the year N, which we know to be a Tuesday.

So there are 565 days in between, Let’s divide 565 by 7.

So the 300th day of year N is 5 days after the 100th day of year N − 1.

Since we are going backwards, we go 5 days before Tuesday.

It’s Thursday!