Gun Duel

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 Rick’s strategy?

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.

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.