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9 vertical lines, 18 horizontal and 22 diagonal lines.
(Of the diagonal lines 6 go from front to back, 6 go from left to right, 6 go from top to bottom while four lines connect the 8 corner cells.)
a total of 49 lines
(27 of length 1, 18 of length Root 2 and 4 of length Root 3)
Tic Tac Toe
Age 11 to 14
Challenge Level 
We received only one correct solution to this problem.
There are only 49 winning lines, which no doubt many of you will find hard to believe. Duplication of lines obviously helped muddy the approaches that were used with this problem.
Laura of West Flegg GM Middle School used an approach which classified the type of winning line possible with accompanying sketches :
9 vertical lines, 18 horizontal and 22 diagonal lines.
(Of the diagonal lines 6 go from front to back, 6 go from left to right, 6 go from top to bottom while four lines connect the 8 corner cells.)
a total of 49 lines
(27 of length 1, 18 of length Root 2 and 4 of length Root 3)
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