Keep moving!

Probability Level 1

You are in (1,1) cell of a 5 × 5 grid . In each step, you can move either one cell right, one cell left, one cell up or one cell down . You have to reach cell (2, 4) in exactly 4 moves. You can't put your leg on cell (1, 3) as it is dangerous. Find number of ways of reaching the destination.

You also can't get out of the grid. There are no other restrictions.

Difficulty: † † † † † \dagger \color{grey}{}\dagger \dagger \dagger \color{grey}{\dagger}

5 2 6 1 7 3 8 4

Aryan Sanghi by Aryan Sanghi , 17, India

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1 solution

Aryan Sanghi
Jun 14, 2020

You have to move 3 steps up and 1 step right to reach out to your destination. This accounts for four moves, and you have exactly that many.

So, you can't afford moving a step left or down in any move.

So, let U denote a move one cell up and R denote a move one cell right.

The possibile combinations are

  • UUUR

  • UURU

  • URUU

  • RUUU

Out of the four combinations, 1 s t ^{st} and 2 n d ^{nd} are eliminated as they require us to step on the (1, 3) cell, which isn't allowed.

So, the answer is 2 \boxed{2}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

There is no way to move right, so the answer is 0 \boxed{0} .

Vinayak Srivastava - 12 months ago

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