Brain Teasers and Puzzles

There is a group of four prisoners, Al, Bill, Chuck, and Dick. After one year in prison, they have a chance to be released. It works as follows. There is a room with a row of four boxes. Slips with the prisoners' names are randomly placed in the boxes, one per box. Each prisoner enters the room, one at a time, checks one or two boxes of their choice, leaves the room without changing anything, and goes to his cell without any communication with other prisoners. Next prisoner enters the room. Etc. If each prisoner finds his names in the boxes he checks, all four are released. If even one of them does not find his name, all four stay in prison for another year…

There is a round table and an unlimited supply of round tokens. Two players place in turn one token at a time anywhere on the table without overlapping other tokens. The last player to place a token, wins. What is a winning strategy?

A car goes 15 mph for 1 mile. How fast must it go in the same 1 mile back to average 30 mph for the entire round trip? *According to a story, Albert Einstein got this puzzle in a letter from a friend and enjoyed the trick.

A string is wound evenly around a circular rod exactly four times. What is the length of the string if the length of the rod is 12 cm, and its circumference is 4 cm?

What fraction of the bottle is full?

During Solar eclipse the Moon shadow moves on the Earth surface. In which direction does it move, toward East or toward West?

You are given four pieces of chain shown on the left, and you want to make a circular chain shown on the right. What is a minimum number of links you need to cut to do the job?

With one cut / line, not necessarily straight, divide this figure into two identical parts:

A capital letter has been cut from a sheet of paper and given a single fold: What letter is it? It could be, but is not an L.

Four bugs sit in a perfect 10x10 square, ABCD. Simultaneously, they start marching: A toward B, B toward C, C toward D, and D toward A. They march, spiraling, until they meet at the center. What distance does each bug cover?

Since I stumbled badly over @Genady shape puzzle, I thought I would dig out this old Victorian number puzzle for him Some here will have seen this one before. Unfortunately I have lost all of the digits except one so I wonder if he can help ? It is a simple long division, presented the English way with the result (quotient) on top. That is a six digit dividend divided by a three digit divisor on the left. There is no remainder. (I believe that some Americans put the quotient on the right not above as I have done). The grid paper is simply there to correctly align the digits.

Mars rover made 100 km South, then 100 km West, and then 100 km North, arriving to the starting point. What was the starting point? This puzzle is easy, but not too easy.

There are 5 bags full of coins which look identical, but all the coins in some bags are real while all the coins in other bags are fake. Real coin weighs 10 g, fake coin weighs 9 g. Using a weighing scale, identify the bags with real and the bags with fake coins by weighing only once. PS. It is also possible that coins in all the bags are real, and that coins in all the bags are fake.

Imagine points on a plane which are vertices of a square 1x1 grid covering the entire plane. Find a shape with area < 1 such that it cannot be placed on the plane without touching at least one of these points.

I've made a mistake by posting this puzzle in the other thread (https://www.scienceforums.net/topic/131412-puzzle-for-the-day/?do=findComment&comment=1239451). It does not belong there. Thus, I repost it here and copy relevant comments from that thread. Hope to continue discussing this puzzle here: @TheVat: Seemed easy. I'm on a tablet so the hidden button doesn't seem to appear. It can be figured without recourse to formulae. @Genady: It is an easy one to make a mistake, too. @TheVat: Spoiler Yep. One has to see there are two kinds of revolving, one with respect to circle B and one with respect to us, looking do…

PS. @Boltzmannbrain, since you seem to like infinities, you might find it interesting.

9x9 magic squares: Is it possible to create a 9x9 magic square that is Pan Magic and Associative. 1. Pan Magic (every row, column, diagonal, and broken diagonal, sum up to the same value) 2. Associative (each pair of numbers symmetrically opposite to the center number sum up to the same value)

Solve the following alphametic puzzle: Replace each letter with unique digit from [0 1 2 3 4 5 6 7 8 9] ADANI + MODI ------ STEAL

A friend has sent this question to me. I have it solved with linear algebra (and some hand waving). Can you find a shorter way to the answer? (It's not a homework, not mine anyway. My homework times long gone.) A gardener collected 17 apples. He finds that each time he removes an apple from his harvest, he can share the remaining fruit in two piles of equal weight, each containing 8 apples. Show that all apples are the same weight.

This question has five parts and needs five answers Cut a cube of side 2 cms into eight identical pieces such that the surface area of each piece is : A. 6 sq cms B. 4 + 2✅2 sq cms C. 5 + 2✅2 sq cms D. 10 sq cms E. 6 + 2✅4.25 sq cms