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+--- Day 13: Claw Contraption ---
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+Next up: the lobby of a resort on a tropical island. The Historians take a moment to admire the hexagonal floor tiles before spreading out.
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+
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+Fortunately, it looks like the resort has a new arcade! Maybe you can win some prizes from the claw machines?
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+The claw machines here are a little unusual. Instead of a joystick or directional buttons to control the claw, these machines have two buttons labeled A and B. Worse, you can't just put in a token and play; it costs 3 tokens to push the A button and 1 token to push the B button.
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+
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+With a little experimentation, you figure out that each machine's buttons are configured to move the claw a specific amount to the right (along the X axis) and a specific amount forward (along the Y axis) each time that button is pressed.
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+Each machine contains one prize; to win the prize, the claw must be positioned exactly above the prize on both the X and Y axes.
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+
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+You wonder: what is the smallest number of tokens you would have to spend to win as many prizes as possible? You assemble a list of every machine's button behavior and prize location (your puzzle input). For example:
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+
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+Button A: X+94, Y+34
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+Button B: X+22, Y+67
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+Prize: X=8400, Y=5400
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+
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+Button A: X+26, Y+66
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+Button B: X+67, Y+21
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+Prize: X=12748, Y=12176
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+
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+Button A: X+17, Y+86
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+Button B: X+84, Y+37
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+Prize: X=7870, Y=6450
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+
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+Button A: X+69, Y+23
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+Button B: X+27, Y+71
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+Prize: X=18641, Y=10279
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+
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+This list describes the button configuration and prize location of four different claw machines.
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+
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+For now, consider just the first claw machine in the list:
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+ Pushing the machine's A button would move the claw 94 units along the X axis and 34 units along the Y axis.
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+ Pushing the B button would move the claw 22 units along the X axis and 67 units along the Y axis.
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+ The prize is located at X=8400, Y=5400; this means that from the claw's initial position, it would need to move exactly 8400 units along the X axis and exactly 5400 units along the Y axis to be perfectly aligned with the prize in this machine.
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+
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+The cheapest way to win the prize is by pushing the A button 80 times and the B button 40 times. This would line up the claw along the X axis (because 80*94 + 40*22 = 8400) and along the Y axis (because 80*34 + 40*67 = 5400). Doing this would cost 80*3 tokens for the A presses and 40*1 for the B presses, a total of 280 tokens.
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+
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+For the second and fourth claw machines, there is no combination of A and B presses that will ever win a prize.
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+
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+For the third claw machine, the cheapest way to win the prize is by pushing the A button 38 times and the B button 86 times. Doing this would cost a total of 200 tokens.
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+
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+So, the most prizes you could possibly win is two; the minimum tokens you would have to spend to win all (two) prizes is 480.
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+
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+You estimate that each button would need to be pressed no more than 100 times to win a prize. How else would someone be expected to play?
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+
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+Figure out how to win as many prizes as possible. What is the fewest tokens you would have to spend to win all possible prizes?
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+
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+Your puzzle answer was 26810.
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+
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+The first half of this puzzle is complete! It provides one gold star: *
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+--- Part Two ---
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+
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+As you go to win the first prize, you discover that the claw is nowhere near where you expected it would be. Due to a unit conversion error in your measurements, the position of every prize is actually 10000000000000 higher on both the X and Y axis!
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+
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+Add 10000000000000 to the X and Y position of every prize. After making this change, the example above would now look like this:
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+
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+Button A: X+94, Y+34
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+Button B: X+22, Y+67
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+Prize: X=10000000008400, Y=10000000005400
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+
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+Button A: X+26, Y+66
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+Button B: X+67, Y+21
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+Prize: X=10000000012748, Y=10000000012176
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+
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+Button A: X+17, Y+86
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+Button B: X+84, Y+37
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+Prize: X=10000000007870, Y=10000000006450
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+
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+Button A: X+69, Y+23
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+Button B: X+27, Y+71
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+Prize: X=10000000018641, Y=10000000010279
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+
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+Now, it is only possible to win a prize on the second and fourth claw machines. Unfortunately, it will take many more than 100 presses to do so.
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+
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+Using the corrected prize coordinates, figure out how to win as many prizes as possible. What is the fewest tokens you would have to spend to win all possible prizes?
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