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”.

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.

Beautiful Tapestry

A piece of a beautiful tapestry is missing. Can you figure out what its colors are?

The tapestry represents the factorizations of the numbers from 2 to 26.

Each 12×12 square on the tapestry represents a number between 2 and 26, such that all squares representing prime numbers are painted in single colors. The colors of the squares representing composite numbers are determined by the factors of these numbers.

The number 2 is represented by orange color (top left corner). The number 3 is represented by green color. The number 4 = 2×2 is represented once again by orange (2, 2) color. The number 5 is represented by red color. The number 6 = 2×3 is represented by orange (2) and green (3) colors. The number 7 is represented by blue color. The number 8 = 2×2×2 is represented once again by orange (2, 2, 2) color. The number 9 =3×3 is represented once again by green (3, 3) color. The number 10 = 2×5 is represented by orange (2) and red (5) colors, and so on.