Colorful Cat's Play

Logic Level 3

Felicia the cat was playing with a pink yarn ball on the room floor of \(7\times7\) square tiles; each row of tiles was colored in the rainbow spectrum: red, orange, yellow, green, blue, indigo, & violet respectively.

While the naughty cat was rolling the ball across the floor, the yarn thread was spun out, leaving its trail on the tiles, where Felicia started from the upper left red corner all the way down to the lower left violet corner in column 1.

To continue the play, Felicia would make an upward track alternating with a downward track in the next right columns, without receding to the left ever. For example, as shown in the picture, after the first move in column 1, it had to move to the next violet tile before making a new upward track. Any up or down-ward track in any column had to cover at least 2 colored tiles, so there was no going horizontally from one column to the next two.

Throughout the play, Felicia crossed each color of the tiles more than once and crossed 2 tiles in 2 non-adjacent columns while the other 5 tracks differed in lengths of tiles. In the end, it finished playing at the lower right violet corner.

If there were only one row that Felicia crossed all 7 tiles of the same color with no groups of over 8 connected uncrossed tiles, which color would that row be?


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