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Gun Duel

Section: Brain Teasers Category: Mathematics

Difficulty: Advanced Tags: Featured, Probability

Mick, Nick, and Rick arrange a three-person gun duel. Mick hits his target 1 out of every 3 times, Nick hits his target 2 out of every 3 times, and Rick hits his target every time. If the three are taking turns shooting at each other, with Mick starting first and Nick second, what should be Mick’s strategy?

SOLUTION

Clearly, Mick should not aim for Nick, because if he kills him, then he will be killed by Rick. Similarly, Nick should not aim for Mick, because if he kills him, then he also will be killed by Rick. Therefore, if Rick ends up against alive Mick and Nick, he will aim at Nick, because he would prefer to face off a weaker opponent afterward. This means that if Nick is alive after Mick shoots, he will shoot at Rick.

Thus, if Mick shoots at Rick and kills him, then he will have to face off Nick with chance of survival less than 1/3. Instead, if he decides to shoot in the air, then he will face off Nick or Rick with chance of survival at least 1/3. Therefore, Mick’s strategy is to keep shooting in the air, until he ends up alone against one of his opponents.

Unknown Author January 16, 2022

4 Comments

The Number in the Yellow Circle

Section: Brain Teasers Category: Insight

Difficulty: Advanced

Which is the missing number in the yellow circle?

SOLUTION

The missing number is 12. Each number is equal to the sum of the digits of the numbers pointing towards it.

Unknown Author January 4, 2022

9 Comments

Vinculus Puzzles

Section: Brain Teasers Category: Deduction

Difficulty: Advanced

Circles are particles and lines joining them are bonds. The objective is to find all the hidden values, following these four rules:

Particle values must be the sum of their bond values.
Particles can have the following values: 0, 1, 2, 4, 8, 12, 16.
Bonds can have the following values: 0, 1, 2, 4.
If two particles have the same value, the bond between them must have value 0.

SOLUTION

The solutions are shown below.

Dr. DJ Upton January 1, 2022

0 Comments

Scoring penalties

Section: Brain Teasers Category: Mathematics

Difficulty: Advanced

At some point in Leonel Messi’s career, the football player had less than 80% success when performing penalty kicks. Later in his career, he had more than 80% success when performing penalty kicks. Show that there was a moment in Leonel Messi’s career when he had exactly 80% success when performing penalty kicks.

SOLUTION

Let us see that it is impossible for Messi to jump from under 80% success rate to over 80% success rate in just one attempt. Indeed, if Messi’s success rate was below 80% after N attempts, then he scored at most 4N/5 – 1/5 = (4N-1)/5 times. If his success rate was above 80% after N+1 attempts, then he scored at least 4(N+1)/5 + 1/5 = (4N-1)/5 + 6/5 times. However, Messi can not score more than one goal in a single attempt, which completes the proof.

Unknown Author December 13, 2021

0 Comments

Five Men in the Rain

Section: Brain Teasers Category: Lateral

Difficulty: Advanced

There were five men going to church and it started to rain. The four that ran got wet and the one that stood still stayed dry.

SOLUTION

Four of the men were carrying a dead man in a coffin to his funeral.

Unknown Author December 10, 2021

4 Comments

Sequence 4, 2, 3, 4

Section: Brain Teasers Category: Insight

Difficulty: Advanced Tags: Sequence

What is the next number in this sequence:

4, 2, 3, 4, 6, 2, 4, ?

SOLUTION

The answer is 8. The numbers represent the lengths of the words in the question:

what → 4
is → 2
the → 3
next → 4
number → 6
in → 2
this → 4
sequence → 8

Unknown Author November 28, 2021

0 Comments

Canals on Mars Maze

Section: Brain Teasers Category: Deduction

Difficulty: Advanced

Starting with the letter “T” at the bottom, visit all spots exactly once before returning to the beginning, so that the letters you pass through spell a complete sentence.

SOLUTION

The path goes through the letters “T”, “H”, “E”, “R”, “E”, “I”, “S”, “N”, “O”, “P”, “O”, “S”, “S”, “I”, “B”, “L”, “E”, “W”, “A”, “Y”, to spell the sentence “There is no possible way”.

Sam Loyd November 22, 2021

0 Comments

53 Bicycles and a Dead Man

Section: Brain Teasers Category: Lateral

Difficulty: Advanced

There is a room with a table, 53 bicycles, and four men. One of the four men is dead. How did he die?

SOLUTION

The “bicycles” are the (famous) Bicycle playing cards. The four men were playing poker, but one of them was cheating with an extra card, so he got killed.

Unknown Author October 25, 2021

2 Comments

Raise Me None

Section: Casual Puzzles Category: Riddle

Difficulty: Advanced

Raise me none and I am unbeaten.
Raise me once and I am excessive.
Raise me twice and I am forward.
Raise me thrice and I am eaten.
All said right, but wrongly spelled.

Who am I?

SOLUTION

The answer is the NUMBER 2:

2⁰ = 1 (“one”), which is unbeaten;
2¹ = 2 (“too”), which is excessive;
2² = 4 (“fore”), which is forward;
2³ = 8 (“ate”), which is eaten.

Unknown Author October 19, 2021

0 Comments

Freezes When Overheated

Section: Casual Puzzles Category: Riddle

Difficulty: Advanced

What freezes when it is overheated?

SOLUTION

The answer is COMPUTER.

Unknown Author October 1, 2021

3 Comments