Turning points was a new puzzle type I created last year as a Mutant on my first Decathlon test. I liked some of the potential the puzzle had, but didn't think I'd fully explored all of its properties, so that was my goal with the two puzzles on the Double Decathlon. The first, with its even/odd theme, should have a pretty interesting path even for an easy puzzle. The second will be a harder nut to crack if you only apply Numberlink thinking. Of course, using every cell is a rule here (and only implied there).

Rules: Draw paths through adjacent white cells connecting each pair of numbers, using every white cell in the grid in exactly one path. The path connecting each number N must contain exactly N turns.

So, these puzzles exploit a few properties of the Turning Points rules that Numberlink does not include. First, the rules say "every cell must be used". Well, in the first puzzle it is going to be pretty hard to use all those cells if you can't find something that can reach into the lower-left corner, below the 2's which will link up somehow. There is a particular "most efficient" packing that you'll need to use.

Another feature that is not so hard to observe in these puzzles, but hasn't necessarily been useful until these, is that the parity of the number indicates whether the start/end direction of each path is the same or different. If an even number starts going up or down, it ends this way too. If an odd number starts going up or down, it ends going left or right at the second number. Well, the 7 and 6 in the middle of this puzzle are pinned, and force a left/right path on the other 6 (not as useful immediately) and a vertical 7 in the lower-left corner (very useful). These seeded paths, plus needing to reach all cells which matters in the corners, will seed a lot of little bits that you need to pack efficiently to find the single solution. I liked the design a lot, and think similar puzzles of this size should hold more fruit in the future.

Easy

Hard

Rules: Draw paths through adjacent white cells connecting each pair of numbers, using every white cell in the grid in exactly one path. The path connecting each number N must contain exactly N turns.

**Easy:****Hard:**So, these puzzles exploit a few properties of the Turning Points rules that Numberlink does not include. First, the rules say "every cell must be used". Well, in the first puzzle it is going to be pretty hard to use all those cells if you can't find something that can reach into the lower-left corner, below the 2's which will link up somehow. There is a particular "most efficient" packing that you'll need to use.

Another feature that is not so hard to observe in these puzzles, but hasn't necessarily been useful until these, is that the parity of the number indicates whether the start/end direction of each path is the same or different. If an even number starts going up or down, it ends this way too. If an odd number starts going up or down, it ends going left or right at the second number. Well, the 7 and 6 in the middle of this puzzle are pinned, and force a left/right path on the other 6 (not as useful immediately) and a vertical 7 in the lower-left corner (very useful). These seeded paths, plus needing to reach all cells which matters in the corners, will seed a lot of little bits that you need to pack efficiently to find the single solution. I liked the design a lot, and think similar puzzles of this size should hold more fruit in the future.

**Solutions:**Easy

Hard

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