Puzzles 67 - Puzzle Prime

The Ping Pong Puzzle

Section: Brain Teasers Category: Deduction

Difficulty: Advanced

Three friends – A, B, and C, are playing ping pong. They play the usual way – two play at a time, the winner stays on the table, the loser lets the third one play. If you know that A played 10 matches in total, B played 15 matches in total, and C played 17 matches in total, who lost the second game?

SOLUTION

A lost it. Since there have been (10 + 15 + 17) / 2 = 21 games played in total, and each player never misses 2 games in a row, the only way for A to play just 10 games is if he plays the 2nd, 4th, 6th, etc. games, and every time loses.

Unknown Author February 26, 2018

1 Comment

The Troll Brothers

Section: Brain Teasers Category: Deduction

Difficulty: Expert

There are four troll brothers – Wudhor, Xhaqan, Yijlob, and Zrowag.

Wudhor always says the truth.
Xhaqan always lies.
Yijlob lies or says the truth unpredictably.
Zrowag is deaf and never answers.

You must ask these brothers four YES/NO questions (one troll per question), and figure out their names. What questions would you ask?

SOLUTION

Coming soon.

Source:

Puzzling StackExchange

Lynn February 25, 2018

7 Comments

Strips in the Plane

Section: Brain Teasers Category: Mathematics

Difficulty: Hard

Prove that you can not cover the plane with infinite strips which have a total sum of their widths equal to 1.

SOLUTION

Take a circle with radius 1 in the plane. A strip with width X covers at most an area of 2X of the circle. Therefore all strips cover at most an area of 2, which is smaller than the total area of the circle (~3.14).

Unknown Author February 17, 2018

0 Comments

Pool Maze

Section: Casual Puzzles Category: Maze

Difficulty: Medium

Find a non-intersecting path between the two holes in this maze, which passes through each of the balls in the given order.

SOLUTION

The solution is shown below.

Dave Phillips February 16, 2018

0 Comments

Shuffling Cards

Section: Brain Teasers Category: Insight

Difficulty: Hard

52 cards – 2 of clubs to Ace of clubs, 2 of diamonds to Ace of diamonds, 2 of hearts to Ace of hearts, and 2 of spades to Ace of spades – are arranged in a deck. We shuffle them in the following manner:

We take the top card and put in a random place inside the deck.
Once we get to the King of spades and put it somewhere in the deck, we stop.

Show that this method shuffles the deck uniformly, i.e. every permutation has the same chance to appear.

SOLUTION

Notice that at all times the cards below the King of spades are shuffled uniformly. Therefore at the end, after we put the King of spades in a random place inside the deck, the entire shuffle will be uniform as well.

Puzzle Prime February 12, 2018

0 Comments

Consistent Polyhedron

Section: Brain Teasers Category: Mathematics

Difficulty: Advanced

Can you construct a convex polyhedron, such that no two of its faces have the same number of edges?

SOLUTION

No, you can not construct such a polyhedron. Assume the opposite and consider its face, which has the largest number of sides, say k. Then the polyhedron contains at least k more faces with different numbers of sides, all less than m. However, this is clearly impossible.

Puzzle Prime February 6, 2018

0 Comments

The Stolen Coins

Section: Brain Teasers Category: Detective

Difficulty: Medium

Someone stole gold coins from a museum near the park. No one saw the thief take the coins, so there isn’t a description of the robber. Slylock Fox suspects one of the creatures in the park is the thief. Which one?

SOLUTION

The raccoon on the seesaw couldn’t hold the heavier bear off the ground unless he was carrying something heavy. Since gold is one of the heaviest metals, Slylock suspects the raccoon is the thief and has hidden the coins in his clothes.

Bob Weber February 5, 2018

5 Comments

Pawns on the Chessboard

Section: Brain Teasers Category: Mathematics

Difficulty: Expert

Six pawns are placed in the middle squares of the main diagonal of a chess board – b7, c6, d5, e4, f3, g2. You are allowed to take any pawn on the chessboard and replace it with two pawns – one on the square above it and one on the square on its right, in case there are empty squares there. If after several moves there are no more pawns on the main diagonal, show that all the squares above it except for h8 are covered by pawns.

SOLUTION

Assign the following weights on the squares of the chessboard:

1 on the main diagonal a8 – h1
1/2 on the diagonal b8 – h2
1/4 on the diagonal c8 – h3
1/8 on the diagonal d8 – h4
1/16 on the diagonal e8 – h5
1/32 on the diagonal f8 – h6
1/64 on the diagonal g8 – h7

Every time you make the splitting move, the total sum of the numbers of the squares covered by pawns remains a constant. At the beginning that sum is 6. Since 7/2 + 6/4 + 5/8 + 4/16+ 3/32 + 2/64 = 6, all 27 squares above the main diagonal, except the top-right corner (on which you can not place a pawn in any way), must be covered by pawns at the end.

Unknown Author January 31, 2018

0 Comments

Monochromatic

Section: Brain Teasers Category: Chess

Difficulty: Advanced

If you know that the following game has been monochromatic, i.e. no piece has moved from black to white square or vice-versa, which one is the correct position of the bishop – e3 or e4?

SOLUTION

The correct position of the bishop is e3. Otherwise, no White’s piece could have captured the last Black’s piece, moving on black squares.

Unknown Author January 30, 2018

0 Comments

On the Lawn

Section: Brain Teasers Category: Lateral

Difficulty: Easy

There are several pieces of coal, a carrot, and a scarf lying on a lawn. If nobody placed them there, how did they end up like that?

SOLUTION

Somebody made a snowman which melted within a few days.

Unknown Author January 29, 2018

0 Comments