Nine tokens are black on one side and white on the other. Initially, four tokens have the black side up. In each turn you have to flip three tokens. What is the least number of turns you need to have all tokens showing the same color?

Question

Bruce Combs

Mathematics

4 June, 16:24

Nine tokens are black on one side and white on the other. Initially, four tokens have the black side up. In each turn you have to flip three tokens. What is the least number of turns you need to have all tokens showing the same color?

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Answers (1)

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Cindy Hurley · Answer 1

2 movements

Step-by-step explanation:

In this case what we will do is name the white chips "W" and the black ones "B". If there are 9 tiles and 4 are in black then the rest, that is 5, in white, like this:

B-B-B-B-W-W-W-W-W

First movement, in turn we can flip 3 tiles, in this case we flip two blacks and one white, it would look like this:

W-W-B-B-B-W-W-W-W

The second movement is to turn the 3 black ones and thus they would all be blank

W-W-W-W-W-W-W-W-W

In other words, the smallest number of movements is 2.