The solution: Tim is 3, Jane is 8, and Mary is 15. A little grumbling is in order here, as clue number 1 leads to the situation a year and a half ago, when Tim was 1 1/2, Jane was 6 1/2, and Mary was 13 1/2.

This sort of problem is easy if you write down a set of equations. Let t be the year that Tim was born, j be the year that Jane was born, m be the year that Mary was born, and y be the current year. As indefinite years come up, let y1, y2, ... be the indefinite years. Then the equations are

y + 10 - t = 2 (y1 - j) y1 - m = 9 (y1 - t)

y - 8 - m = 1/2 (y2 - j) y2 - j = 1 + y3 - t y3 - m = 5 (y + 2 - t)

t + 1 - m = 3 + y4 - t y4 - j = 3 (y5 - 6 - m) y5 - j = 1/2 (y6 - t) y6 - m = 10 + y7 - m y7 - j = 1/3 (y8 - t) y8 - m = 3 (j - m)

t = y - 3 j = y - 8 m = y - 15

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