Gun Duel

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

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

Now if Mick shoots at Nick and kills him, then he will have to face off Rick with chance of survival less than 1/3. Instead, if he decides to shoot in the air, then he will face off Rick or Nick 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.

Vinculus Puzzles

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

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

The solutions are shown below.

Scoring penalties

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.

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.

Canals on Mars Maze

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.

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”.

Canaries in Space

NASA was considering sending canaries into space to study them under zero gravity. The project was scrapped when someone realized that in spite of having sufficient water supplies, they could die of dehydration within a few hours. Why?

Unlike humans, birds need gravity in order to swallow. Thus, in space they wouldn’t be able to drink and will die of dehydration.

Raise Me None

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?

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.