Puzzles...That I Liked

Three thieves came to the left side of a river. Each thief has two big suitcases. A thief does not want to leave his suitcase with any other person, but it is OK to leave suitcases on a bank with no people there. They have a boat, which can fit all three of them without suitcases or two persons with a suitcase or one person with two suitcases. How can they all get to the other side with all the luggage?

This puzzle is from the collection of river crossing puzzles by Alexander Shapovalov.

Solution

Alice, Betty, and Carol took the same series of examinations. There was one grade of A, one grade of B, and one grade of C for each examination, where A, B, C are different positive integers. The final test scores were

Alice: 20
Betty: 10
Carol: 9

If Betty placed first in the arithmetic examination, who placed second in the spelling examination?

(Assume that no two students got the same grade in same examination.)

The puzzle appeared in the 16th International Mathematical Olympiad, Erfurt-Berlin, July 1974.

Solution

At a work picnic, Todd announces a challenge to his coworkers. Bruce and Ava are selected to play first. Todd places Rs.100 on a table and explains the game. Bruce and Ava will each draw a random card from a standard 52-card deck. Each will hold that card to his/her forehead for the other person to see, but neither can see his/her own card. The players may not communicate in any way. Bruce and Ava will each write down a guess for the color of his/her own card, i.e. red or black. If either one of them guesses correctly, they both win Rs.50. If they are both incorrect, they lose. He gives Bruce and Ava five minutes to devise a strategy beforehand by which they can guarantee that they each walk away with the Rs.50.

Bruce and Ava complete their game and Todd announces the second level of the game. He places Rs.200 on the table. He tells four of his coworkers -- Emily, Charles, Doug and Fran—that they will play the same game, except this time guessing the suit of their own card, i.e. clubs, hearts, diamonds or spades. Again, Todd has the four players draw cards and place them on their foreheads so that each player can see the other three players' cards, but not his/her own. Each player writes down a guess for the suit of his/her own card. If at least one of them guesses correctly, they each win Rs.50. There is no communication while the game is in progress, but they have five minutes to devise a strategy beforehand by which they can be guaranteed to walk away with Rs.50 each.

For each level of play – 2 players or 4 players– how can the players ensure that someone in the group always guesses correctly?

This puzzle appeared in the August 2016 issue of NSA's The Puzzle Periodical. It was created by Ben H., a Systems Engineer at the NSA.

Solution

• 4, 6, X, 9, 10, 12, 14, 15, 16
• 1, 2, 6, 24, 120, X, 5040, 40320, 362880
• 2, X, 3, 4, 7
• 1, 2, 3, 4, 5, 6, X, 8, 9, 153, 370, 371
• X, 2, 3, 4, 5, 6, 7
• 6, 28, 496, 8128, X, 8589869056, 137438691328
• 0, 1, 1, X, 4, 7, 13, 24, 44, 81

This puzzle is without instructions — figuring out what needs to be done is part of the fun. Solvers are allowed to use the Internet and any available tools. The answer to this puzzle is a word.

This is a puzzle by Tanya Khovanova. You can find it in her blog.

Solution:

In a bag of sixteen coins, eight are heavier than the rest. Eight coins weigh 11 grams each while the other eight coins weigh 10 grams each. We do not know which coin is which, but one coin is marked as a “Platinum Jubilee” coin. Can we figure out whether the Platinum Jubilee coin is heavier or lighter using a balance scale at most three times?

Solution

You have a small and a large hourglasses. The small one can measure 5 minutes and the large one can measure 7 minutes. How can you measure 16 minutes with 2 hourglasses running together?

Solution

A football pitch is 100 metres long. A piece of bunting 101 metres long is tied to the base of the two corner flags along one side of the pitch. When the bunting is lifted at the middle of the pitch, will the players be able to?

[note: the bunting is non-elastic, and is raised until it is taut.]

Source: Alex Bellos's Monday puzzle

Solution