Hello everyone!
Recently, I was solving Chapter 13: Divisibility and Primes from Manhattan 5lb. There, I came across a question that was quite confusing. I’m sharing the question and my approach below.
I solved it like this: Tue…to…Mon is one complete cycle of 7 days. Therefore, 100/7= approx 14. something. This means 14 full cycles of 7 days, which means on the 98th day, the 14th cycle will be completed. And our 98th day is Mon. Likewise, the 100th day will be Wednesday.
Does 100 days later mean Thursday, which is the 101st day?
Yes, if that’s how u like to count it then sure. Since it says “100 days later”, I would personally just ignore the starting day (Tuesday) and follow the same logic you have mentioned. 98 days lands you to Tuesday as well and thus 100 days later occurs on a Thursday.
I couldn’t quite get the logic of skipping Tuesday.
Let’s suppose we want to find a unit digit for 2^38. It repeats in the pattern of four (2,4,8,6,2,4…). Here, 2^36 means nine complete cycles of 4 terms. Therefore 2^38 = 4. Here, we are not skipping the series’s first term, ‘2’.
Ah, i’m saying where you start doesn’t change the “cyclicity issue”. If you start with 2^6 having unit digit of 4 then every “cycle of 4” from2^6 will have the same unit digit. There’s no compulsion for me to start at 2^1.
For your specific problem, since we’re counting “days later” it’s better to skip tuesday (the starting day) itself. One day later would correspond to Wednesday instead of thinking of “day 2” by including the starting day, which apparently doesn’t help us at all. Anyway, since we start on Tuesday (but don’t count it), any “number” of weeks later would still leave you on a Tuesday.
100 leaves a remainder of 2 when divided by 7, so you’re just counting 2 days ahead of Tuesday to get your desired answer of Thursday.
