Please include parity I have tried many methods but it does not work Please help

I have ten copies of each of the twelve pentominoes. Can I use all of them to completely tile twelve 5 x 10 rectangles?

Let S be a function such that S(N) is the sum of digits of N. N belongs to natural numbers, and N < 10²³. Find the number of N that satisfies the equation: S(N) = S(S(N))

I'm wondering if there's a way to disguise the total rotation of a cube. For example, if I wanted to rotate the (solved) cube I could obviously just apply a 90 degree yaw rotation,however, I would like it so that the rubiks cube gets scrambled and unscrambled in the process. For example take the ...

Patrick and Rachel go to a tennis tournament with 7 other couples. Each round is a single's match (1 vs 1). Nobody plays against his partner and nobody plays twice with the same player. At the end of the tournament Patrick asked everyone how many people they played against, and found that each on...

A barrel contains 10l of whiskey, another one contains 10l of coca-cola. If I do the following operation in two steps: 1 step) with a glass I transfer 200ml of whiskey from the first barrel to the second one, and I mix the barrel very well. 2 step) After that, with a glass I transfer 200ml of the...

Letters from Gladys are geography-themed standalone crosswords. Each puzzle has five thematic answers, which are places, sights or landmarks in or around a certain location (in this case, an autonomous community). Each thematic answer is notable enough to have its own article in the English Wiki...

Romeo and Juliet try to meet each other everyday at a certain place between 12:00 and 13:00. They arrive at the place at a random time between 12:00 and 13:00 and they wait 15 minutes (but never after 13:00), if nobody shows up they come back home. Everyday, which is the probability that they mee...

Sum of digits of numbers I recently posted this puzzle, I'm not sure why it is not well received. How can I make sure that this does not happen next time?

I don't know the answer to this question, but after having spent some time trying to solve, I suspect it is impossible. (Hopefully I didn't miss something really obvious...) I'm hoping someone can supply a proof!

To date, on Puzzling.SE I have contributed (counting: 10, 20, 30...) 99 problems to the site. So to mark my 100th, here's a massive meta-puzzle to celebrate the occasion! Task Solve the nine sub-puzzles and meta-puzzle featured in the image below to find the final 9-letter answer. Partial answe...

https://i.stack.imgur.com/KTRkF.jpg What does this weird equation relate to in the picture. How can we make sense of the equation and rights now