Day 13

2024/day13/challenge

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+--- Day 13: Claw Contraption ---
+
+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.
+
+Fortunately, it looks like the resort has a new arcade! Maybe you can win some prizes from the claw machines?
+
+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.
+
+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.
+
+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.
+
+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:
+
+Button A: X+94, Y+34
+Button B: X+22, Y+67
+Prize: X=8400, Y=5400
+
+Button A: X+26, Y+66
+Button B: X+67, Y+21
+Prize: X=12748, Y=12176
+
+Button A: X+17, Y+86
+Button B: X+84, Y+37
+Prize: X=7870, Y=6450
+
+Button A: X+69, Y+23
+Button B: X+27, Y+71
+Prize: X=18641, Y=10279
+
+This list describes the button configuration and prize location of four different claw machines.
+
+For now, consider just the first claw machine in the list:
+
+    Pushing the machine's A button would move the claw 94 units along the X axis and 34 units along the Y axis.
+    Pushing the B button would move the claw 22 units along the X axis and 67 units along the Y axis.
+    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.
+
+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.
+
+For the second and fourth claw machines, there is no combination of A and B presses that will ever win a prize.
+
+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.
+
+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.
+
+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?
+
+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?
+
+Your puzzle answer was 37128.
+--- Part Two ---
+
+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!
+
+Add 10000000000000 to the X and Y position of every prize. After making this change, the example above would now look like this:
+
+Button A: X+94, Y+34
+Button B: X+22, Y+67
+Prize: X=10000000008400, Y=10000000005400
+
+Button A: X+26, Y+66
+Button B: X+67, Y+21
+Prize: X=10000000012748, Y=10000000012176
+
+Button A: X+17, Y+86
+Button B: X+84, Y+37
+Prize: X=10000000007870, Y=10000000006450
+
+Button A: X+69, Y+23
+Button B: X+27, Y+71
+Prize: X=10000000018641, Y=10000000010279
+
+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.
+
+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?
+
+Your puzzle answer was 74914228471331.
+
+Both parts of this puzzle are complete! They provide two gold stars: **

2024/day13/code.py

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+#!/usr/bin/env python3
+
+import sys, re
+from sympy import solve
+from sympy.abc import x, y
+
+
+def prizes(a, b, prize):
+    sols = solve([a[0] * x + b[0] * y - prize[0], a[1] * x + b[1] * y - prize[1]], x, y, dict=True)
+    if len(sols) > 1: print('help!', sols)
+    if int(sols[0][x]) != sols[0][x] or int(sols[0][y]) != sols[0][y]: return 0
+    else: return 3*sols[0][x]+sols[0][y]
+
+
+if __name__ == '__main__':
+    cms = open(sys.argv[1]).read().split('\n\n')
+    res1, res2 = 0, 0
+    for cm in cms:
+        g = re.search(r'Button A: X\+(?P<xa>\d+), Y\+(?P<ya>\d+)\nButton B: X\+(?P<xb>\d+), Y\+(?P<yb>\d+)\nPrize: X=(?P<px>\d+), Y=(?P<py>\d+)', cm)
+        button_a = (int(g['xa']), int(g['ya']))
+        button_b = (int(g['xb']), int(g['yb']))
+        prize = (int(g['px']), int(g['py']))
+        res1 += prizes(button_a, button_b, prize)
+        prize = (prize[0]+10000000000000, prize[1]+10000000000000)
+        res2 += prizes(button_a, button_b, prize)
+
+    # challenge 1
+    print(f"challenge 1:\n{res1}\n")
+
+    # challenge 2
+    print(f"challenge 2:\n{res2}")
+

2024/day13/example

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+Button A: X+94, Y+34
+Button B: X+22, Y+67
+Prize: X=8400, Y=5400
+
+Button A: X+26, Y+66
+Button B: X+67, Y+21
+Prize: X=12748, Y=12176
+
+Button A: X+17, Y+86
+Button B: X+84, Y+37
+Prize: X=7870, Y=6450
+
+Button A: X+69, Y+23
+Button B: X+27, Y+71
+Prize: X=18641, Y=10279