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PLS HELP ILL GIVE BRAINLIEST AND 20 POINts

The square shown is divided into five cells. Starting at any cell, how many paths can be drawn that move only to adjacent cells and that include all five cells?

PLS HELP ILL GIVE BRAINLIEST AND 20 POINts The square shown is divided into five cells Starting at any cell how many paths can be drawn that move only to adjace class=

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Answer:

150 (not sure)

Step-by-step explanation:

Paths that only touch 5 points unrepeatedly:

I used a tree diagram to list all the workable paths, taking cell A as an example:

  • ABCDE
  • ABCED
  • ABECD
  • ABEDC
  • AEBCD
  • AEDCB
  • ADCBE
  • ADCEB
  • ADEBC
  • ADECB

2*(3x2 - 1) = 10

When you start at A you would have 3 choices, but after that only two, and since DB or BD can't happen and crossing B and D for the second step is the same, I double it.

Paths that touch 5 points and reapeat one of them:

2*(3x2x2 - 1x2) = 20

Paths that touch 5 points and repeat two of them:

2*(3x2x2x2-1x2x2) = 40

Paths that touch 5 points and repeat three of them:

2*(3x2x2x2x2-1x2x2x2) = 80

The sum of the answers in these 4 senarios is the final answer.

150

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