Lovers Meet - Part 2

Probability Level 1

Anna and Ben live at opposite corners of a 2 by 3 block.
If Anna only moves right or up or down, and isn't allowed to retrace her steps, how many ways does she have to get to Ben?

2 3 4 5

Chung Kevin by Chung Kevin , 45, Australia

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2 solutions

We can count manually:

  1. Down → \rightarrow Across 2

  2. Across 2 → \rightarrow Down

  3. Across → \rightarrow Down → \rightarrow Across

  4. Down → \rightarrow Across → \rightarrow Up → \rightarrow Across → \rightarrow Down

Or we can calculate: Since the perimeter of the 2 blocks are 6 6 , simply multiply it's factorial:

2 ! × 1 ! × 2 ! × 1 ! = 4 2!\times 1! \times 2!\times 1!=\boxed{4}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Noor MAlik
Jul 5, 2015

Initially she can move right or down.
If she moves to right, she can go right->down or down->right.
If she moves down-> right, she can go up->right->down or right.
So, total ways 4 \boxed{4}


0 Helpful 0 Interesting 0 Brilliant 0 Confused

Is there a simpler explanation that doesn't require case checking?

Chung Kevin - 5 years, 11 months ago

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I'm really sure there is one for nxn case. But I'm too lazy to figure it out. Sorry :) hehe

Noor MAlik - 5 years, 11 months ago

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