Daily (ish) puzzles worth scribbling on a napkin.

There is a prime number p such that 16p + 1 is the cube of a positive integer. Find p.

Anh read a book. On the first day she read n pages in t minutes, where n and t are positive integers. On the second day Anh read n+1 pages in t+1 minutes. Each day thereafter Anh read one more page than she read on the previous day, and it took her one more minute than on the previous day until she completely read the 374 page book. It took her a total of 319 minutes to read the book. Find n + t.

Two dice appear to be standard dice with faces numbered 1 to 6, but each die is weighted so that the probability of rolling the number k is directly proportional to k. The probability of rolling a 7 with this pair of dice is m / n where m and n are relatively prime positive integers. Find m+n.

You have a cup of coffee and a cup of milk with equal volumes. You scoop one spoon of coffee into the milk, stir, and then scoop a spoon of the mixture back into the coffee. Which cup ends up with more of the other liquid?

Show that no matter how many times you fold a rectangular piece of paper (only perfectly in half each time), the ratio of its sides always remains rational.