Spencer had four arrows. He hit the target with all four shots. With each shot he could have scored 25 points, 10 points, 5 points, or 1 point. How many total scores are possible?

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Each shot can get any of the 4 scores.

If there was only one shot, then number of total scores possible = 4 = 4^1

They are 1, 5, 10 and 25

If there was were 2 shots, then number of total scores possible = 4 + 4 + 4 + 4 = 16 = 4^2

They are

1 + 1, 1 + 5, 1 + 10, 1 + 25

5 + 1, 5 + 5, 5 + 10, 5 + 25

10 + 1, 10 + 5, 10 + 10, 10 + 25

25 + 1, 25 + 5, 25 + 10, 25 + 25

So, for 4 shots the possible number of total scores = 4^4 = 256

ANSWER: 256 total scores are possible

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