From a814f5fc07c5d7fab59651c8ff32525caa329852 Mon Sep 17 00:00:00 2001
From: narimiran <narimiran@disroot.org>
Date: Fri, 13 Dec 2024 13:39:11 +0100
Subject: [PATCH] day 13

---
 clojure/day13.clj                 |  214 +++++
 clojure/tests/solutions_tests.clj |    3 +-
 index.md                          |    1 +
 inputs/13.txt                     | 1279 +++++++++++++++++++++++++++++
 inputs/13_test.txt                |   15 +
 5 files changed, 1511 insertions(+), 1 deletion(-)
 create mode 100644 clojure/day13.clj
 create mode 100644 inputs/13.txt
 create mode 100644 inputs/13_test.txt

diff --git a/clojure/day13.clj b/clojure/day13.clj
new file mode 100644
index 0000000..7fc1c2a
--- /dev/null
+++ b/clojure/day13.clj
@@ -0,0 +1,214 @@
+^{:nextjournal.clerk/visibility {:code :hide :result :hide}}
+(ns day13
+  {:nextjournal.clerk/auto-expand-results? true
+   :nextjournal.clerk/toc :collapsed}
+  (:require
+   aoc
+   [nextjournal.clerk :as clerk]))
+
+
+;; # Day 13: Claw Contraption
+;;
+;; Today we're on a tropical island, and in the lobby of a resort there are
+;; lots of claw machines.\
+;; They have two buttons, `A` and `B`, which move the claw different amount
+;; in the x- and y- directions.
+;; We win a prize if, after N amount of presses, we are at the exact
+;; x-y location of the prize.
+;;
+;; For example:
+;;
+(def 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")
+
+
+;; Here we have four different machines.\
+;; To press button `A` we need 3 tokens, to press button `B` we need 1 token.
+;; Our task is to find the minimum amount of tokens needed to win all
+;; possible prizes (on some machines it is impossible to win a prize).
+
+
+
+
+
+;; ## Input parsing
+;;
+;; Each machine is in its own paragraph, so the `aoc/parse-paragraphs`
+;; function will come handy.
+;; The description format is always the same, and we're only interested
+;; in the numbers for each machine:
+;;
+(defn parse-data [input]
+  (aoc/parse-paragraphs input :ints))
+
+(def example-data (parse-data example))
+(def data (parse-data (aoc/read-input 13)))
+
+
+
+
+;; ## Math
+;;
+;; The task for Part 1 says:
+;; > You estimate that each button would need to be pressed no more
+;; > than **100 times** to win a prize.
+;;
+;; Which, if you're familiar with AoC, looks like a bait.
+;; You should immediately get a hint that for Part 2 the numbers will be
+;; much higher and we won't be able to check every single combination
+;; until we find a solution.
+;;
+;; For each machine, we need to solve a system of two equations with
+;; two unknowns:
+;; ```
+;; ax*a + bx*b = px
+;; ay*a + by*b = py
+;; ```
+;; where `a` and `b` are unknown amounts of button presses for button `A`
+;; and button `B`, respectively.\
+;; For each machine, `ax` and `ay` are the movements for each press of
+;; button `A`, and `bx` and `by` are the movements for button `B`.
+;; The prize is at `[px py]`.
+;;
+;; At first, I solved these equations on paper, manually doing the
+;; subtitutions.
+;;
+;; There is another way (well, it is the same stuff, just written/calculated
+;; a bit differently).
+;; This system can also been written as:
+;;
+^{:nextjournal.clerk/visibility {:code :hide}}
+(clerk/tex "
+\\begin{bmatrix}
+a_x & b_x \\\\
+a_y & b_y
+\\end{bmatrix}
+\\begin{bmatrix}
+a \\\\
+b
+\\end{bmatrix}
+=
+\\begin{bmatrix}
+p_x \\\\
+p_y
+\\end{bmatrix}
+")
+
+
+;; We can solve this system using
+;; [Cramer's rule](https://en.wikipedia.org/wiki/Cramer's_rule#Applications).
+;; (Last time I've used it, I was in highschool, 20+ years ago!)
+;;
+;; We need to find three determinants:
+;; - `det-M`, determinant of the original matrix
+;; - `det-a`, we substitute `ax` and `ay` in the original matrix with
+;;   `px` and `py` and find a determinant
+;; - `det-b`, we substitute `bx` and `by` in the original matrix with
+;;   `px` and `py` and find a determinant
+;;
+^{:nextjournal.clerk/visibility {:code :hide}}
+(clerk/tex "
+{\\det}_M
+=
+\\begin{vmatrix}
+a_x & b_x \\\\
+a_y & b_y
+\\end{vmatrix}
+
+\\hspace{1 cm}
+
+{\\det}_a
+=
+\\begin{vmatrix}
+p_x & b_x \\\\
+p_y & b_y
+\\end{vmatrix}
+
+\\hspace{1 cm}
+
+{\\det}_b
+=
+\\begin{vmatrix}
+a_x & p_x \\\\
+a_y & p_y
+\\end{vmatrix}
+")
+
+;; To get the solution for `a` and `b`, we need to divide the determinants:
+;; `det-a / det-M` and `det-b / det-M`, respectively.
+
+
+
+
+
+
+;; ## Solution
+;;
+;; We have all we need to solve the equations.
+;;
+;; For our task, valid solutions are only those for which `a` and `b` are integers.
+;; (We cannot press a button 0.1 times :P).\
+;; If a solution is valid, we multiply the presses of button `A` by their
+;; price of 3 tokens, and add presses of `B` (costing 1 token):
+;;
+(defn det [a1 a2 b1 b2]
+  (- (* a1 b2) (* b1 a2)))
+
+(defn solve-eq [pos-incr [[ax ay] [bx by] [px py]]]
+  (let [px (+ pos-incr px)
+        py (+ pos-incr py)
+        det-M (det ax ay bx by)
+        det-a (det px py bx by)
+        det-b (det ax ay px py)
+        a (/ det-a det-M)
+        b (/ det-b det-M)]
+    (if (or (ratio? a) (ratio? b))
+      0
+      (+ (* 3 a) b))))
+
+
+;; The only difference between Part 1 and Part 2 is that for the second part
+;; we need to increase the coordinates of a prize by `10000000000000` in
+;; each direction:
+;;
+(defn solve [data]
+  (vec
+   (for [pos-incr [0 10000000000000]]
+     (aoc/sum-map (partial solve-eq pos-incr) data))))
+
+
+(solve example-data)
+(solve data)
+
+
+
+
+
+;; ## Conclusion
+;;
+;; Today was mainly a math task.
+;;
+;; If you know how to solve a system of two linear equations with two unknowns,
+;; the hardest thing to code (if you don't have some helpers ready ;))
+;; is to separate the input into different groups and parse integers in each.
+
+
+
+
+^{:nextjournal.clerk/visibility {:code :hide :result :hide}}
+(defn -main [input]
+  (let [data (parse-data input)]
+    (solve data)))
diff --git a/clojure/tests/solutions_tests.clj b/clojure/tests/solutions_tests.clj
index 5267968..ac1f7be 100644
--- a/clojure/tests/solutions_tests.clj
+++ b/clojure/tests/solutions_tests.clj
@@ -2,7 +2,7 @@
   (:require
    day01 day02 day03 day04 day05
    day06 day07 day08 day09 day10
-   day11 day12 ;day13 day14 day15
+   day11 day12 day13 ;day14 day15
    ;; day16 day17 day18 day19 day20
    ;; day21 day22 day23 day24 day25
    [clojure.test :refer [deftest is run-tests successful?]]))
@@ -35,6 +35,7 @@
 (check-day 10 [36 81] [820 1786])
 (check-day 11 [55312 65601038650482] [183435 218279375708592])
 (check-day 12 [1930 1206] [1464678 877492])
+(check-day 13 [480 875318608908] [27105 101726882250942])
 
 
 (let [summary (run-tests)]
diff --git a/index.md b/index.md
index 3ac9e45..86bae0f 100644
--- a/index.md
+++ b/index.md
@@ -65,4 +65,5 @@ Task  | Notebook  | Comment
 [Day 10: Hoof It](https://adventofcode.com/2024/day/10) | [day10.clj](clojure/day10) | Finally some pathfinding!
 [Day 11: Plutonian Pebbles](https://adventofcode.com/2024/day/11) | [day11.clj](clojure/day11) | Episode VI: Return of the Lanternfish
 [Day 12: Garden Groups](https://adventofcode.com/2024/day/12) | [day12.clj](clojure/day12) | Turns = sides.
+[Day 13: Claw Contraption](https://adventofcode.com/2024/day/13) | [day13.clj](clojure/day13) | Kosmo Cramer!
 
diff --git a/inputs/13.txt b/inputs/13.txt
new file mode 100644
index 0000000..34be663
--- /dev/null
+++ b/inputs/13.txt
@@ -0,0 +1,1279 @@
+Button A: X+54, Y+22
+Button B: X+36, Y+62
+Prize: X=19754, Y=14184
+
+Button A: X+20, Y+68
+Button B: X+34, Y+13
+Prize: X=15660, Y=15792
+
+Button A: X+63, Y+17
+Button B: X+11, Y+28
+Prize: X=2658, Y=11605
+
+Button A: X+15, Y+56
+Button B: X+74, Y+29
+Prize: X=9393, Y=11622
+
+Button A: X+34, Y+97
+Button B: X+83, Y+35
+Prize: X=3876, Y=4197
+
+Button A: X+14, Y+62
+Button B: X+75, Y+27
+Prize: X=12989, Y=4061
+
+Button A: X+46, Y+17
+Button B: X+15, Y+54
+Prize: X=15841, Y=336
+
+Button A: X+19, Y+61
+Button B: X+69, Y+12
+Prize: X=204, Y=7413
+
+Button A: X+34, Y+14
+Button B: X+29, Y+40
+Prize: X=2353, Y=10368
+
+Button A: X+64, Y+32
+Button B: X+25, Y+48
+Prize: X=3273, Y=304
+
+Button A: X+18, Y+60
+Button B: X+66, Y+30
+Prize: X=11594, Y=2330
+
+Button A: X+65, Y+47
+Button B: X+11, Y+29
+Prize: X=4677, Y=195
+
+Button A: X+13, Y+23
+Button B: X+42, Y+14
+Prize: X=7115, Y=12417
+
+Button A: X+81, Y+55
+Button B: X+26, Y+93
+Prize: X=2703, Y=5678
+
+Button A: X+50, Y+96
+Button B: X+74, Y+20
+Prize: X=8694, Y=9856
+
+Button A: X+19, Y+54
+Button B: X+74, Y+36
+Prize: X=6145, Y=9170
+
+Button A: X+45, Y+76
+Button B: X+43, Y+15
+Prize: X=4194, Y=5627
+
+Button A: X+28, Y+91
+Button B: X+94, Y+48
+Prize: X=2282, Y=2009
+
+Button A: X+70, Y+35
+Button B: X+33, Y+83
+Prize: X=4786, Y=3856
+
+Button A: X+14, Y+89
+Button B: X+38, Y+40
+Prize: X=2186, Y=3415
+
+Button A: X+55, Y+19
+Button B: X+43, Y+79
+Prize: X=4737, Y=2757
+
+Button A: X+32, Y+76
+Button B: X+60, Y+17
+Prize: X=11124, Y=5467
+
+Button A: X+33, Y+62
+Button B: X+50, Y+21
+Prize: X=4940, Y=12625
+
+Button A: X+56, Y+14
+Button B: X+48, Y+92
+Prize: X=2888, Y=962
+
+Button A: X+14, Y+58
+Button B: X+83, Y+30
+Prize: X=6249, Y=5488
+
+Button A: X+47, Y+83
+Button B: X+47, Y+11
+Prize: X=7153, Y=15685
+
+Button A: X+35, Y+68
+Button B: X+52, Y+16
+Prize: X=12241, Y=14956
+
+Button A: X+46, Y+72
+Button B: X+56, Y+25
+Prize: X=6054, Y=4401
+
+Button A: X+35, Y+57
+Button B: X+43, Y+14
+Prize: X=10516, Y=12390
+
+Button A: X+29, Y+56
+Button B: X+41, Y+25
+Prize: X=6288, Y=2319
+
+Button A: X+73, Y+19
+Button B: X+59, Y+86
+Prize: X=9965, Y=8669
+
+Button A: X+13, Y+43
+Button B: X+49, Y+13
+Prize: X=12137, Y=19559
+
+Button A: X+17, Y+65
+Button B: X+67, Y+22
+Prize: X=1910, Y=15266
+
+Button A: X+55, Y+27
+Button B: X+11, Y+43
+Prize: X=7767, Y=5007
+
+Button A: X+26, Y+18
+Button B: X+35, Y+94
+Prize: X=4719, Y=9616
+
+Button A: X+37, Y+81
+Button B: X+58, Y+13
+Prize: X=11010, Y=1876
+
+Button A: X+66, Y+43
+Button B: X+17, Y+88
+Prize: X=6227, Y=5057
+
+Button A: X+36, Y+66
+Button B: X+61, Y+31
+Prize: X=1642, Y=10702
+
+Button A: X+54, Y+17
+Button B: X+15, Y+50
+Prize: X=17444, Y=2332
+
+Button A: X+33, Y+74
+Button B: X+47, Y+16
+Prize: X=1127, Y=13206
+
+Button A: X+45, Y+93
+Button B: X+84, Y+43
+Prize: X=9867, Y=10858
+
+Button A: X+35, Y+99
+Button B: X+64, Y+33
+Prize: X=3780, Y=5511
+
+Button A: X+29, Y+62
+Button B: X+46, Y+24
+Prize: X=14412, Y=6932
+
+Button A: X+91, Y+18
+Button B: X+21, Y+20
+Prize: X=9303, Y=2474
+
+Button A: X+61, Y+34
+Button B: X+30, Y+75
+Prize: X=6835, Y=7015
+
+Button A: X+32, Y+82
+Button B: X+46, Y+12
+Prize: X=7126, Y=14580
+
+Button A: X+30, Y+47
+Button B: X+36, Y+11
+Prize: X=13922, Y=14563
+
+Button A: X+79, Y+39
+Button B: X+12, Y+43
+Prize: X=15040, Y=13839
+
+Button A: X+15, Y+14
+Button B: X+20, Y+81
+Prize: X=1075, Y=1502
+
+Button A: X+35, Y+80
+Button B: X+45, Y+11
+Prize: X=10380, Y=11870
+
+Button A: X+50, Y+36
+Button B: X+21, Y+58
+Prize: X=4389, Y=3546
+
+Button A: X+31, Y+95
+Button B: X+60, Y+14
+Prize: X=5432, Y=4076
+
+Button A: X+96, Y+20
+Button B: X+64, Y+77
+Prize: X=3424, Y=2687
+
+Button A: X+15, Y+51
+Button B: X+60, Y+26
+Prize: X=1505, Y=19741
+
+Button A: X+37, Y+12
+Button B: X+33, Y+78
+Prize: X=10344, Y=13604
+
+Button A: X+70, Y+93
+Button B: X+84, Y+21
+Prize: X=9184, Y=8034
+
+Button A: X+33, Y+85
+Button B: X+99, Y+59
+Prize: X=4356, Y=2988
+
+Button A: X+26, Y+27
+Button B: X+13, Y+60
+Prize: X=1105, Y=3240
+
+Button A: X+55, Y+31
+Button B: X+21, Y+46
+Prize: X=7181, Y=11070
+
+Button A: X+20, Y+54
+Button B: X+41, Y+32
+Prize: X=2979, Y=3400
+
+Button A: X+35, Y+19
+Button B: X+33, Y+60
+Prize: X=10334, Y=11024
+
+Button A: X+84, Y+21
+Button B: X+29, Y+79
+Prize: X=9575, Y=6340
+
+Button A: X+58, Y+24
+Button B: X+15, Y+64
+Prize: X=10518, Y=6264
+
+Button A: X+41, Y+12
+Button B: X+45, Y+69
+Prize: X=10120, Y=8966
+
+Button A: X+87, Y+28
+Button B: X+14, Y+67
+Prize: X=6242, Y=6571
+
+Button A: X+12, Y+28
+Button B: X+65, Y+24
+Prize: X=1515, Y=12044
+
+Button A: X+85, Y+24
+Button B: X+29, Y+37
+Prize: X=7600, Y=2434
+
+Button A: X+34, Y+92
+Button B: X+94, Y+69
+Prize: X=9882, Y=12282
+
+Button A: X+11, Y+37
+Button B: X+23, Y+12
+Prize: X=848, Y=8448
+
+Button A: X+52, Y+28
+Button B: X+33, Y+63
+Prize: X=3429, Y=6843
+
+Button A: X+57, Y+13
+Button B: X+56, Y+55
+Prize: X=4314, Y=1744
+
+Button A: X+81, Y+24
+Button B: X+12, Y+59
+Prize: X=13487, Y=6933
+
+Button A: X+72, Y+50
+Button B: X+15, Y+40
+Prize: X=8927, Y=9290
+
+Button A: X+68, Y+27
+Button B: X+16, Y+30
+Prize: X=2728, Y=2904
+
+Button A: X+66, Y+13
+Button B: X+54, Y+65
+Prize: X=6060, Y=1846
+
+Button A: X+56, Y+86
+Button B: X+88, Y+44
+Prize: X=5840, Y=4138
+
+Button A: X+44, Y+80
+Button B: X+46, Y+15
+Prize: X=15084, Y=8430
+
+Button A: X+50, Y+18
+Button B: X+13, Y+60
+Prize: X=6386, Y=6944
+
+Button A: X+15, Y+63
+Button B: X+67, Y+14
+Prize: X=12210, Y=802
+
+Button A: X+22, Y+65
+Button B: X+65, Y+33
+Prize: X=2817, Y=4983
+
+Button A: X+23, Y+37
+Button B: X+51, Y+11
+Prize: X=4351, Y=1387
+
+Button A: X+58, Y+39
+Button B: X+14, Y+50
+Prize: X=2678, Y=3343
+
+Button A: X+13, Y+80
+Button B: X+65, Y+68
+Prize: X=4784, Y=5536
+
+Button A: X+47, Y+93
+Button B: X+84, Y+33
+Prize: X=5496, Y=3948
+
+Button A: X+51, Y+13
+Button B: X+21, Y+58
+Prize: X=13064, Y=14007
+
+Button A: X+38, Y+22
+Button B: X+12, Y+26
+Prize: X=1962, Y=11422
+
+Button A: X+51, Y+13
+Button B: X+34, Y+62
+Prize: X=13062, Y=2106
+
+Button A: X+31, Y+11
+Button B: X+44, Y+78
+Prize: X=4550, Y=7654
+
+Button A: X+97, Y+27
+Button B: X+48, Y+63
+Prize: X=10321, Y=3816
+
+Button A: X+59, Y+17
+Button B: X+27, Y+78
+Prize: X=978, Y=18744
+
+Button A: X+68, Y+27
+Button B: X+25, Y+64
+Prize: X=2115, Y=1002
+
+Button A: X+19, Y+33
+Button B: X+91, Y+19
+Prize: X=7873, Y=2689
+
+Button A: X+39, Y+96
+Button B: X+47, Y+16
+Prize: X=5548, Y=8672
+
+Button A: X+58, Y+11
+Button B: X+20, Y+80
+Prize: X=4668, Y=4086
+
+Button A: X+13, Y+33
+Button B: X+56, Y+14
+Prize: X=3696, Y=1396
+
+Button A: X+21, Y+45
+Button B: X+34, Y+13
+Prize: X=15420, Y=12003
+
+Button A: X+12, Y+22
+Button B: X+77, Y+27
+Prize: X=2487, Y=1477
+
+Button A: X+58, Y+89
+Button B: X+70, Y+19
+Prize: X=5774, Y=1787
+
+Button A: X+25, Y+63
+Button B: X+53, Y+13
+Prize: X=13823, Y=19135
+
+Button A: X+45, Y+36
+Button B: X+34, Y+99
+Prize: X=6416, Y=9369
+
+Button A: X+81, Y+35
+Button B: X+18, Y+50
+Prize: X=4203, Y=5025
+
+Button A: X+81, Y+28
+Button B: X+12, Y+58
+Prize: X=2592, Y=5258
+
+Button A: X+57, Y+21
+Button B: X+19, Y+67
+Prize: X=19310, Y=9410
+
+Button A: X+62, Y+48
+Button B: X+25, Y+84
+Prize: X=1505, Y=2652
+
+Button A: X+98, Y+18
+Button B: X+20, Y+26
+Prize: X=9334, Y=1960
+
+Button A: X+23, Y+42
+Button B: X+33, Y+13
+Prize: X=11779, Y=4858
+
+Button A: X+12, Y+36
+Button B: X+75, Y+39
+Prize: X=4355, Y=8495
+
+Button A: X+20, Y+34
+Button B: X+37, Y+18
+Prize: X=10274, Y=2754
+
+Button A: X+89, Y+26
+Button B: X+18, Y+44
+Prize: X=4524, Y=1864
+
+Button A: X+11, Y+36
+Button B: X+53, Y+21
+Prize: X=18093, Y=17453
+
+Button A: X+48, Y+22
+Button B: X+47, Y+74
+Prize: X=8784, Y=8868
+
+Button A: X+29, Y+53
+Button B: X+45, Y+16
+Prize: X=12465, Y=10268
+
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+Button A: X+67, Y+43
+Button B: X+11, Y+36
+Prize: X=4764, Y=9202
+
+Button A: X+21, Y+62
+Button B: X+54, Y+22
+Prize: X=4434, Y=2234
+
+Button A: X+89, Y+87
+Button B: X+24, Y+88
+Prize: X=6501, Y=7323
+
+Button A: X+54, Y+29
+Button B: X+28, Y+51
+Prize: X=13224, Y=17258
+
+Button A: X+62, Y+45
+Button B: X+39, Y+94
+Prize: X=4796, Y=9262
+
+Button A: X+45, Y+23
+Button B: X+12, Y+52
+Prize: X=11084, Y=11636
+
+Button A: X+22, Y+37
+Button B: X+48, Y+25
+Prize: X=5514, Y=11182
+
+Button A: X+15, Y+38
+Button B: X+75, Y+39
+Prize: X=16520, Y=17711
+
+Button A: X+78, Y+11
+Button B: X+49, Y+92
+Prize: X=9365, Y=6341
+
+Button A: X+98, Y+14
+Button B: X+13, Y+64
+Prize: X=5741, Y=2498
+
+Button A: X+13, Y+63
+Button B: X+61, Y+20
+Prize: X=13770, Y=14824
+
+Button A: X+21, Y+38
+Button B: X+62, Y+37
+Prize: X=17864, Y=15513
+
+Button A: X+24, Y+21
+Button B: X+15, Y+62
+Prize: X=1476, Y=4224
+
+Button A: X+16, Y+75
+Button B: X+52, Y+12
+Prize: X=468, Y=8849
+
+Button A: X+14, Y+41
+Button B: X+46, Y+22
+Prize: X=2040, Y=1353
+
+Button A: X+49, Y+16
+Button B: X+29, Y+54
+Prize: X=10446, Y=18614
+
+Button A: X+11, Y+69
+Button B: X+75, Y+18
+Prize: X=10963, Y=2327
+
+Button A: X+37, Y+64
+Button B: X+47, Y+20
+Prize: X=18201, Y=3324
+
+Button A: X+99, Y+14
+Button B: X+87, Y+75
+Prize: X=14862, Y=6177
+
+Button A: X+12, Y+58
+Button B: X+82, Y+33
+Prize: X=7438, Y=6507
+
+Button A: X+72, Y+13
+Button B: X+13, Y+79
+Prize: X=14160, Y=11952
+
+Button A: X+24, Y+55
+Button B: X+73, Y+39
+Prize: X=12196, Y=4761
+
+Button A: X+47, Y+28
+Button B: X+21, Y+52
+Prize: X=969, Y=9732
+
+Button A: X+57, Y+29
+Button B: X+15, Y+30
+Prize: X=17750, Y=13700
+
+Button A: X+40, Y+23
+Button B: X+13, Y+26
+Prize: X=13248, Y=14881
+
+Button A: X+68, Y+13
+Button B: X+85, Y+90
+Prize: X=9707, Y=6207
+
+Button A: X+47, Y+23
+Button B: X+19, Y+57
+Prize: X=2226, Y=13254
diff --git a/inputs/13_test.txt b/inputs/13_test.txt
new file mode 100644
index 0000000..912f482
--- /dev/null
+++ b/inputs/13_test.txt
@@ -0,0 +1,15 @@
+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