Puzzle on Number Game to Save Life

Number Game Puzzle

Damon and Mason enjoy playing puzzles on number games to save a life. puzzle. However, if Mason loses the game, he would die. Whoever screams out “101” first, from Damon and Mason, wins. Mason is desperate to win this game because he is on the run for his life.

Premise – Damon and Mason alternate calling out a number from 1 to n.

Rules – While playing the game, they adhere to the following guidelines:

  1. They can begin the game by dialing a number between 1 and 10.
  2. The next person in line should dial a number by increasing the last number by one to ten, inclusive.

Objective – Can you assist him by advising him on the best plan for winning the game?

Puzzle on Number Game to save life

Solution of Number Game to Save Life Puzzle

As we know, Mason prefers to call 101 first. Let us look at the given steps for this scenario:-

  • He can do this if, Damon will be calling any integer between 91 and 100 (both inclusive), which he will do if he dials 90.
  • If Damon calls any integer between 80 and 89 (both inclusive), which will happen if he calls 79, he can continue ahead.
  • If he continues in this manner, he will discover that he should dial 101, 90 (=101-11), 79 (=90-11), 68 (=79-11), and so on.
  • Reverse, starting with 2, let’s suppose Damon calls the least one ahead, i.e. 3, then they alternately call 13, 14, 24, 25, 35, 36, 46, 47, 57, 58, 68, 69, 79, 90, 91, 101.
  • If the number is multiplied by ten each time, the result is 101-2, which is an odd factor of ten.
  • Mason will begin at the odd turn and end at the odd turn.

Based on the foregoing two reasons, you may conclude that the best method for saving his life is for him to begin the game by dialing 2.

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