It's a Race

Probability Level 3

You are about to spell the word RACECAR. Starting from the letter R at the center, you are only allowed to move to an adjacent square for the next letter until you are finished.

In how many ways can you spell it?

Clarification: You are allowed to move to a square already visited.

The answer is 76.

1 solution

Geoff Pilling
Feb 8, 2017

For each of the four corner E's there is one way to make RACECAR. For each of the eight edge E's there are $3\cdot 3= 9$ ways. (Since there are $3$ ways to get there and $3$ ways to get back)

So, that's a total of $4\cdot 1 + 8\cdot 9 = \boxed{76}$ ways.

Seems like many people get stumped by this problem.

The easiest approach is to count the number of ways to each E, square that term, and then sum up these values.

Chung Kevin - 4 years, 4 months ago

Level 5?!:)

Dan Ley - 4 years, 3 months ago

The correct rate is surprising low. I don't know why people are getting stumped by this problem.

Maybe because It's slightly tedious to count carefully?

Chung Kevin - 4 years, 3 months ago

The counting is not at all stressful compared to some things, I liked this problem:) Not sure, maybe they saw the original rating and thought it would be too hard to attempt...

Dan Ley - 4 years, 3 months ago

It was quite eady once u get hold of it..just ignore 4 far e and then multiply how many ways u can jump to one word to another

Partho Kunda - 4 years, 3 months ago

Then add 4. Beacause u only one way if u touch 4 far e

Partho Kunda - 4 years, 3 months ago

It's a Race

The answer is 76.

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