Puzzle Archives - Puzzle Prime

Unfaithful

Section: Brain Teasers Category: Deduction

Difficulty: Medium

Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

Yes
No
Cannot be determined

SOLUTION

The answer is YES. If Anne is unmarried, then Jack is married and is looking at an unmarried person. If not, then she is married and is looking at an unmarried person.

Unknown Author August 22, 2019

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Invisible King

Section: Brain Teasers Category: Chess

Difficulty: Expert

The white king has made himself invisible. Where is he?

SOLUTION

The white king is on c3. Since he cannot be currently on b3 (he will be in double check from the black rook and the black bishop), Black must be currently in check from the white bishop. That’s possible only if White has given a discovered check with his king. That’s possible only if on the previous move, the white king was on b3 and was in double check. The only possible way for this to happen is if Black gave two discovered checks at the same time. The one way to do this is if a black pawn on b4 captured a white pawn on c3 using en passant. Thus after b4xc3, the white king has just captured the black pawn on c3, and that is where he is currently hiding.

Raymond Smullyan August 19, 2019

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Group of Three

Section: Casual Puzzles Category: Riddle

Difficulty: Advanced

I give you a group of three. One is sitting down, and will never get up. The second eats as much as is given to him, yet is always hungry. The third goes away and never returns. What is this group of three?

SOLUTION

The answer is STOVE, FIRE, SMOKE.

Unknown Author August 16, 2019

2 Comments

Product

Section: Brain Teasers Category: Insight

Difficulty: Easy

What is the product (x – a)(x – b)…(x – z) equal to?

SOLUTION

This product is equal to (x – a)(x – b)…(x – x)(x – y)(x – z) = 0.

Puzzle Prime August 13, 2019

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Puzzle Sum 17

Section: Casual Puzzles Category: Rebus

Difficulty: Easy

What American city does this sum spell?
What American state does this sum spell?

SOLUTION

CAN + TON = CANTON
INDIAN + ARAB + BIT – RABBIT = INDIANA

Sam Loyd August 7, 2019

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Space Traffic

Section: Casual Puzzles Category: Maze

Difficulty: Easy

Help the police hunt down the red robot on the run. On the way, try to find:

one red-domed roof; two yellow-capped chimneys;
three red-rimmed chimneys;
a skyscraper with four triangle-topped roofs;
a road that branches into five paths.

SOLUTION

The solution is shown below.

Theo Guignard August 4, 2019

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Move Move Chess

Section: Brain Teasers Category: Insight

Difficulty: Medium

Consider a chess game in which every player is allowed to move twice per turn. Show that Black does not have a winning strategy.

SOLUTION

Assume Black has a winning strategy. Then if White plays Kb1-Kc3 and Kc3-b1 on his first turn, the game basically will start all over again, but with Black moving first. Therefore White will have a winning strategy, which is a contradiction.

Puzzle Prime August 1, 2019

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Codex Enigmatum

Section: Brain Teasers Category: Insight

Difficulty: Advanced

These are a few enigmas from the puzzle book CODEX ENIGMATUM. What is the answer to puzzle #9?

SOLUTION

Puzzle #2 After turning the first wheel 22 times to the right, then 19 times to the left, then 15 times to the right, and finally 11 times to the left, the final wheel will spell the word EXIT.
Puzzle #3 The total number of spots on the hidden sides of the die on the left is 6, which corresponds to the sixth letter in the alphabet – F. Therefore, the four dice on the right correspond to the letters K, I, N, G.
Puzzle #4 In the mosaic on the right, you can find a little star which contains pieces with letters H, I, D, E.
Puzzle #6 If you trace the signature on the paper, starting from the large C, you will pass through the letters C, O, N, T, I, N, U, O, U, S.
Puzzle #8 The picture on the left and the answer to puzzle #6 (“continuous”) suggest that we have to consider the images on the right which can be drawn continuously, without taking off the pencil from the paper or passing through any segment twice. These images are labeled with the letters N, O, S, E.
Puzzle #9 The first 2 letters from the word NOSE spell NO. The last letter from the word EXIT is T. The first letter from the word HIDE is H. The last three letters from the word KING spell ING. When you combine all of them, you get the word NOTHING.

Source:

Codex Enigmatum by Rami Hansenne

Rami Hansenne August 1, 2019

2 Comments

Moms’ Talk

Section: Brain Teasers Category: Mathematics

Difficulty: Hard Tags: Probability

Two moms, Sarah and Courtney, are talking to each other.

Sarah: I have two children.
What is the probability that both of Sarah’s children are boys?

Courtney: Me too! Do you have any boys?
What is the probability that both of Courtney’s children are boys?

Sarah: Yes, I do! What is your younger child?
What is the probability that both of Sarah’s children are boys?

Courtney: It is a boy. He is so mischievous!
What is the probability that both of Courtney’s children are boys?

Sarah: Is he Sagittarius? Sagittarius boys are known to drive their mothers crazy. I can testify from personal experience.
What is the probability that both of Sarah’s children are boys?

Courtney: No, but actually I have the opposite personal experience to yours.
What is the probability that both of Courtney’s children are boys?

Sarah: Well, I guess astrology does not always get it right.

Courtney: I assume it does about half of the time.

SOLUTION

The answers are: ~1/4, ~1/4, ~1/3, ~1/2, ~23/47, 1.

Explanation:

Initially, we do not have any information about the children and therefore the chance that both of them boys is 1/2 × 1/2. This applies to the first and the second question.

After Sarah says that she has at least one boy, there are equal possibilities that she has Boy + Boy, Boy + Girl, or Girl + Boy. Therefore, the chance that both children are boys is 1/3.

After Courtney says that her younger child is a boy, the only remaining question is what is the gender of her older child, and therefore the chance is 1/2.

The fifth exchange implies that Sarah has a Sagittarius boy. There are 23 combinations such that both children are boys and at least one of them is Sagittarius. There are 47 combinations such that at least one of the children is a Sagittarius boy. Therefore, the chance that both children are boys is 23/47.

Finally, Courtney says that her younger child, which is a boy, is not Sagittarius, but her personal experience with Sagittarius boys is positive. Therefore, her older child is a Sagittarius boy and the chance is 1.

Puzzle Prime July 28, 2019

4 Comments

10 Pounds of Flour

Section: Brain Teasers Category: Insight

Difficulty: Medium

You have a big bag of flour, two 5lbs weights, and an inaccurate balance scale. How can you measure exactly 10lbs of flour?

SOLUTION

Put both weights on one side, then fill the other side with flour so that the scale balances out. Then remove the weights and replace them with flour so that the balance scale is balanced again. The amount of flour you put there is exactly 10lbs.

Unknown Author July 25, 2019

11 Comments