[2024] [Day 24]: Crossed Wires

[victoraugustofd]

Challenge description

You and The Historians arrive at the edge of a large grove somewhere in the jungle. After the last incident, the Elves installed a small device that monitors the fruit. While The Historians search the grove, one of them asks if you can take a look at the monitoring device; apparently, it's been malfunctioning recently.

The device seems to be trying to produce a number through some boolean logic gates. Each gate has two inputs and one output. The gates all operate on values that are either true (1) or false (0).

• AND gates output 1 if both inputs are 1; if either input is 0, these gates output 0.
• OR gates output 1 if one or both inputs is 1; if both inputs are 0, these gates output 0.
• XOR gates output 1 if the inputs are different; if the inputs are the same, these gates output 0.

Gates wait until both inputs are received before producing output; wires can carry 0, 1 or no value at all. There are no loops; once a gate has determined its output, the output will not change until the whole system is reset. Each wire is connected to at most one gate output, but can be connected to many gate inputs.

Rather than risk getting shocked while tinkering with the live system, you write down all of the gate connections and initial wire values (your puzzle input) so you can consider them in relative safety. For example:

x00: 1
x01: 1
x02: 1
y00: 0
y01: 1
y02: 0

x00 AND y00 -> z00
x01 XOR y01 -> z01
x02 OR y02 -> z02

Because gates wait for input, some wires need to start with a value (as inputs to the entire system). The first section specifies these values. For example, x00: 1 means that the wire named x00 starts with the value 1 (as if a gate is already outputting that value onto that wire).

The second section lists all of the gates and the wires connected to them. For example, x00 AND y00 -> z00 describes an instance of an AND gate which has wires x00 and y00 connected to its inputs and which will write its output to wire z00.

In this example, simulating these gates eventually causes 0 to appear on wire z00, 0 to appear on wire z01, and 1 to appear on wire z02.

Ultimately, the system is trying to produce a number by combining the bits on all wires starting with z. z00 is the least significant bit, then z01, then z02, and so on.

In this example, the three output bits form the binary number 100 which is equal to the decimal number 4.

Here's a larger example:

x00: 1
x01: 0
x02: 1
x03: 1
x04: 0
y00: 1
y01: 1
y02: 1
y03: 1
y04: 1

ntg XOR fgs -> mjb
y02 OR x01 -> tnw
kwq OR kpj -> z05
x00 OR x03 -> fst
tgd XOR rvg -> z01
vdt OR tnw -> bfw
bfw AND frj -> z10
ffh OR nrd -> bqk
y00 AND y03 -> djm
y03 OR y00 -> psh
bqk OR frj -> z08
tnw OR fst -> frj
gnj AND tgd -> z11
bfw XOR mjb -> z00
x03 OR x00 -> vdt
gnj AND wpb -> z02
x04 AND y00 -> kjc
djm OR pbm -> qhw
nrd AND vdt -> hwm
kjc AND fst -> rvg
y04 OR y02 -> fgs
y01 AND x02 -> pbm
ntg OR kjc -> kwq
psh XOR fgs -> tgd
qhw XOR tgd -> z09
pbm OR djm -> kpj
x03 XOR y03 -> ffh
x00 XOR y04 -> ntg
bfw OR bqk -> z06
nrd XOR fgs -> wpb
frj XOR qhw -> z04
bqk OR frj -> z07
y03 OR x01 -> nrd
hwm AND bqk -> z03
tgd XOR rvg -> z12
tnw OR pbm -> gnj

After waiting for values on all wires starting with z, the wires in this system have the following values:

bfw: 1
bqk: 1
djm: 1
ffh: 0
fgs: 1
frj: 1
fst: 1
gnj: 1
hwm: 1
kjc: 0
kpj: 1
kwq: 0
mjb: 1
nrd: 1
ntg: 0
pbm: 1
psh: 1
qhw: 1
rvg: 0
tgd: 0
tnw: 1
vdt: 1
wpb: 0
z00: 0
z01: 0
z02: 0
z03: 1
z04: 0
z05: 1
z06: 1
z07: 1
z08: 1
z09: 1
z10: 1
z11: 0
z12: 0

Combining the bits from all wires starting with z produces the binary number 0011111101000. Converting this number to decimal produces 2024.

Simulate the system of gates and wires. What decimal number does it output on the wires starting with z?

Challenge input

x00: 1
x01: 1
x02: 1
x03: 1
x04: 1
x05: 0
x06: 0
x07: 0
x08: 0
x09: 0
x10: 1
x11: 0
x12: 0
x13: 1
x14: 1
x15: 1
x16: 1
x17: 0
x18: 1
x19: 1
x20: 0
x21: 1
x22: 1
x23: 0
x24: 0
x25: 1
x26: 1
x27: 0
x28: 1
x29: 1
x30: 0
x31: 1
x32: 1
x33: 1
x34: 1
x35: 0
x36: 0
x37: 1
x38: 1
x39: 0
x40: 1
x41: 0
x42: 0
x43: 1
x44: 1
y00: 1
y01: 0
y02: 0
y03: 1
y04: 1
y05: 1
y06: 0
y07: 0
y08: 1
y09: 1
y10: 0
y11: 1
y12: 0
y13: 0
y14: 0
y15: 0
y16: 0
y17: 1
y18: 1
y19: 0
y20: 0
y21: 1
y22: 0
y23: 1
y24: 1
y25: 0
y26: 0
y27: 0
y28: 0
y29: 0
y30: 1
y31: 0
y32: 1
y33: 1
y34: 1
y35: 1
y36: 0
y37: 0
y38: 1
y39: 1
y40: 0
y41: 0
y42: 1
y43: 1
y44: 1

rdf XOR nck -> z21
y12 AND x12 -> stn
twb XOR jgm -> z41
cpj OR tgr -> cmt
y17 XOR x17 -> jws
cpg XOR tdr -> z14
x42 AND y42 -> dkt
jmq OR bjv -> dck
wkt AND jgp -> cwk
fmk OR wqh -> pqr
jws AND rmd -> rsd
y32 AND x32 -> rns
twb AND jgm -> kvg
nrq XOR wcd -> z09
btc OR rns -> dtb
ctq XOR gjs -> z20
dqd XOR hhm -> z18
hfh AND jdt -> nhs
rsd OR rgp -> hhm
x19 AND y19 -> kmw
dck XOR ctg -> z15
pqr AND hhv -> trm
y08 AND x08 -> trg
x31 AND y31 -> z31
x14 AND y14 -> bjv
y26 XOR x26 -> sbn
pgj XOR fnn -> z30
hwb AND rgq -> cqf
ctq AND gjs -> fcj
thp OR qdg -> rgq
y03 AND x03 -> mhg
sbt XOR ndc -> z05
nrr OR hfv -> dvh
x07 AND y07 -> djc
dtb AND mpb -> hvw
pwm OR cqf -> cjs
dkt OR wdw -> fpv
x24 AND y24 -> djv
vsq OR gkt -> cfp
x17 AND y17 -> rgp
rvf OR vph -> nhg
x44 XOR y44 -> bbf
cjs XOR gnb -> z29
y30 XOR x30 -> pgj
y27 XOR x27 -> sjb
fpp AND bbf -> dps
ggc OR ptt -> fpp
x18 XOR y18 -> dqd
y19 XOR x19 -> jgp
wkt XOR jgp -> z19
jcs XOR ngk -> z04
y21 XOR x21 -> rdf
spp OR fkm -> wkt
x16 XOR y16 -> vsd
y14 XOR x14 -> cpg
mbk OR qwg -> rmd
y10 AND x10 -> nrr
x05 XOR y05 -> sbt
y13 XOR x13 -> fvp
gdf OR tnw -> srm
x09 AND y09 -> gdf
nvc OR rpv -> jdt
kmw OR cwk -> ctq
vsd AND wmb -> qwg
x44 AND y44 -> mfg
y27 AND x27 -> qdg
jbg OR jqp -> ndc
x04 XOR y04 -> ngk
hfh XOR jdt -> z12
ctg AND dck -> sqh
jww XOR djk -> z23
dtf XOR vjq -> z32
ngd AND sbf -> ksc
mfg OR dps -> z45
x01 XOR y01 -> rtg
tdr AND cpg -> jmq
y28 AND x28 -> pwm
y41 AND x41 -> hhf
qqp OR hfd -> fgs
wmb XOR vsd -> z16
pgj AND fnn -> hfd
dmf XOR nwb -> z40
rfs AND pcb -> ktf
y05 AND x05 -> rtp
vjq AND dtf -> btc
fvp AND hjm -> qrk
mpb XOR dtb -> z33
y12 XOR x12 -> hfh
cmt AND cbv -> jcd
tkf AND frw -> nrt
wcd AND nrq -> tnw
hwk AND cbc -> btk
hhv XOR pqr -> dvq
rfq OR bbk -> nwb
nhf OR fcj -> nck
rww XOR kbg -> z42
x11 XOR y11 -> hnn
fgs XOR ctw -> dmh
y36 XOR x36 -> rbf
y01 AND x01 -> vph
fjg XOR fpv -> z43
x06 XOR y06 -> pcb
x33 AND y33 -> spv
y00 XOR x00 -> z00
x23 XOR y23 -> djk
x22 AND y22 -> mjp
wbm AND hrv -> dwv
hwb XOR rgq -> z28
x03 XOR y03 -> wbm
x00 AND y00 -> drq
x23 AND y23 -> dnp
wmk OR kfq -> fnn
x33 XOR y33 -> mpb
y43 XOR x43 -> fjg
y02 XOR x02 -> btp
hnn XOR dvh -> rpv
cpf XOR btf -> z24
y42 XOR x42 -> rww
gps AND ggb -> qvj
sbn AND cmn -> ntc
x36 AND y36 -> gkt
y39 XOR x39 -> vnt
dnp OR nsp -> btf
rtp OR qms -> rfs
y29 AND x29 -> wmk
x24 XOR y24 -> cpf
rtg AND drq -> rvf
sjb AND dbd -> thp
bbf XOR fpp -> z44
x32 XOR y32 -> vjq
vnt AND dvq -> rfq
btf AND cpf -> stf
hjm XOR fvp -> z13
rmd XOR jws -> z17
rfs XOR pcb -> z06
fgs AND ctw -> bmm
vnt XOR dvq -> z39
dvv AND cfp -> wqh
mfj OR vgr -> jgm
y25 AND x25 -> qds
qds OR btk -> cmn
kvh AND srm -> hfv
y09 XOR x09 -> wcd
y10 XOR x10 -> kvh
dwv OR mhg -> jcs
y16 AND x16 -> mbk
y43 AND x43 -> ggc
x34 AND y34 -> krw
x29 XOR y29 -> gnb
y02 AND x02 -> mgr
fgk AND sqm -> mbg
y40 XOR x40 -> dmf
y08 XOR x08 -> frw
dvh AND hnn -> z11
y35 AND x35 -> qvt
qvj OR qvt -> fps
x30 AND y30 -> qqp
nwb AND dmf -> vgr
x31 XOR y31 -> ctw
kvg OR hhf -> kbg
sbf XOR ngd -> z34
mjp OR jcd -> jww
srm XOR kvh -> z10
y15 AND x15 -> ctg
y34 XOR x34 -> ngd
bvk OR trm -> z38
dmh OR bmm -> dtf
x20 XOR y20 -> gjs
y26 AND x26 -> dsw
y04 AND x04 -> jqp
cjs AND gnb -> kfq
rtg XOR drq -> z01
ngk AND jcs -> jbg
ktf OR vpn -> sqm
nhs OR stn -> hjm
y37 AND x37 -> fmk
y13 AND x13 -> rmq
dsw OR ntc -> dbd
hwk XOR cbc -> z25
fgk XOR sqm -> z07
y28 XOR x28 -> hwb
x11 AND y11 -> nvc
mst OR mgr -> hrv
wbm XOR hrv -> z03
gps XOR ggb -> z35
mbg OR djc -> tkf
y20 AND x20 -> nhf
rdf AND nck -> tgr
fps XOR rbf -> z36
x15 XOR y15 -> rpb
sqh OR rpb -> wmb
spv OR hvw -> sbf
y18 AND x18 -> spp
rww AND kbg -> wdw
fpv AND fjg -> ptt
x40 AND y40 -> mfj
y07 XOR x07 -> fgk
y06 AND x06 -> vpn
x22 XOR y22 -> cbv
stf OR djv -> cbc
x38 XOR y38 -> hhv
hhm AND dqd -> fkm
frw XOR tkf -> z08
x37 XOR y37 -> dvv
qrk OR rmq -> tdr
x35 XOR y35 -> ggb
sbt AND ndc -> qms
x21 AND y21 -> cpj
cbv XOR cmt -> z22
nrt OR trg -> nrq
btp AND nhg -> mst
ksc OR krw -> gps
x25 XOR y25 -> hwk
fps AND rbf -> vsq
x39 AND y39 -> bbk
btp XOR nhg -> z02
x41 XOR y41 -> twb
sjb XOR dbd -> z27
sbn XOR cmn -> z26
cfp XOR dvv -> z37
djk AND jww -> nsp
x38 AND y38 -> bvk

Challenge year

2024

[victoraugustofd]

Challenge link

https://adventofcode.com/2024/day/24