Part 1
Description
This year, Santa brought little Bobby Tables a set of wires and bitwise logic gates! Unfortunately, little Bobby is a little under the recommended age range, and he needs help assembling the circuit.Each wire has an identifier (some lowercase letters) and can carry a 16-bit signal (a number from
0 to 65535).
A signal is provided to each wire by a gate, another wire, or some
specific value. Each wire can only get a signal from one source, but can
provide its signal to multiple destinations. A gate provides no signal
until all of its inputs have a signal.The included instructions booklet describes how to connect the parts together:
x AND y -> z means to connect wires x and y to an AND gate, and then connect its output to wire z.For example:
123 -> xmeans that the signal123is provided to wirex.x AND y -> zmeans that the bitwise AND of wirexand wireyis provided to wirez.p LSHIFT 2 -> qmeans that the value from wirepis left-shifted by2and then provided to wireq.NOT e -> fmeans that the bitwise complement of the value from wireeis provided to wiref.
OR (bitwise OR) and RSHIFT (right-shift). If, for some reason, you'd like to emulate the circuit instead, almost all programming languages (for example, C, JavaScript, or Python) provide operators for these gates.For example, here is a simple circuit:
123 -> x
456 -> y
x AND y -> d
x OR y -> e
x LSHIFT 2 -> f
y RSHIFT 2 -> g
NOT x -> h
NOT y -> i
d: 72
e: 507
f: 492
g: 114
h: 65412
i: 65079
x: 123
y: 456
a?Input
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| NOT dq -> dr | |
| kg OR kf -> kh | |
| ep OR eo -> eq | |
| 44430 -> b | |
| NOT gs -> gt | |
| dd OR do -> dp | |
| eg AND ei -> ej | |
| y AND ae -> ag | |
| jx AND jz -> ka | |
| lf RSHIFT 2 -> lg | |
| z AND aa -> ac | |
| dy AND ej -> el | |
| bj OR bi -> bk | |
| kk RSHIFT 3 -> km | |
| NOT cn -> co | |
| gn AND gp -> gq | |
| cq AND cs -> ct | |
| eo LSHIFT 15 -> es | |
| lg OR lm -> ln | |
| dy OR ej -> ek | |
| NOT di -> dj | |
| 1 AND fi -> fj | |
| kf LSHIFT 15 -> kj | |
| NOT jy -> jz | |
| NOT ft -> fu | |
| fs AND fu -> fv | |
| NOT hr -> hs | |
| ck OR cl -> cm | |
| jp RSHIFT 5 -> js | |
| iv OR jb -> jc | |
| is OR it -> iu | |
| ld OR le -> lf | |
| NOT fc -> fd | |
| NOT dm -> dn | |
| bn OR by -> bz | |
| aj AND al -> am | |
| cd LSHIFT 15 -> ch | |
| jp AND ka -> kc | |
| ci OR ct -> cu | |
| gv AND gx -> gy | |
| de AND dk -> dm | |
| x RSHIFT 5 -> aa | |
| et RSHIFT 2 -> eu | |
| x RSHIFT 1 -> aq | |
| ia OR ig -> ih | |
| bk LSHIFT 1 -> ce | |
| y OR ae -> af | |
| NOT ca -> cb | |
| e AND f -> h | |
| ia AND ig -> ii | |
| ck AND cl -> cn | |
| NOT jh -> ji | |
| z OR aa -> ab | |
| 1 AND en -> eo | |
| ib AND ic -> ie | |
| NOT eh -> ei | |
| iy AND ja -> jb | |
| NOT bb -> bc | |
| ha OR gz -> hb | |
| 1 AND cx -> cy | |
| NOT ax -> ay | |
| ev OR ew -> ex | |
| bn RSHIFT 2 -> bo | |
| er OR es -> et | |
| eu OR fa -> fb | |
| jp OR ka -> kb | |
| ea AND eb -> ed | |
| k AND m -> n | |
| et RSHIFT 3 -> ev | |
| et RSHIFT 5 -> ew | |
| hz RSHIFT 1 -> is | |
| ki OR kj -> kk | |
| NOT h -> i | |
| lv LSHIFT 15 -> lz | |
| as RSHIFT 1 -> bl | |
| hu LSHIFT 15 -> hy | |
| iw AND ix -> iz | |
| lf RSHIFT 1 -> ly | |
| fp OR fv -> fw | |
| 1 AND am -> an | |
| ap LSHIFT 1 -> bj | |
| u LSHIFT 1 -> ao | |
| b RSHIFT 5 -> f | |
| jq AND jw -> jy | |
| iu RSHIFT 3 -> iw | |
| ih AND ij -> ik | |
| NOT iz -> ja | |
| de OR dk -> dl | |
| iu OR jf -> jg | |
| as AND bd -> bf | |
| b RSHIFT 3 -> e | |
| jq OR jw -> jx | |
| iv AND jb -> jd | |
| cg OR ch -> ci | |
| iu AND jf -> jh | |
| lx -> a | |
| 1 AND cc -> cd | |
| ly OR lz -> ma | |
| NOT el -> em | |
| 1 AND bh -> bi | |
| fb AND fd -> fe | |
| lf OR lq -> lr | |
| bn RSHIFT 3 -> bp | |
| bn AND by -> ca | |
| af AND ah -> ai | |
| cf LSHIFT 1 -> cz | |
| dw OR dx -> dy | |
| gj AND gu -> gw | |
| jg AND ji -> jj | |
| jr OR js -> jt | |
| bl OR bm -> bn | |
| gj RSHIFT 2 -> gk | |
| cj OR cp -> cq | |
| gj OR gu -> gv | |
| b OR n -> o | |
| o AND q -> r | |
| bi LSHIFT 15 -> bm | |
| dy RSHIFT 1 -> er | |
| cu AND cw -> cx | |
| iw OR ix -> iy | |
| hc OR hd -> he | |
| 0 -> c | |
| db OR dc -> dd | |
| kk RSHIFT 2 -> kl | |
| eq LSHIFT 1 -> fk | |
| dz OR ef -> eg | |
| NOT ed -> ee | |
| lw OR lv -> lx | |
| fw AND fy -> fz | |
| dz AND ef -> eh | |
| jp RSHIFT 3 -> jr | |
| lg AND lm -> lo | |
| ci RSHIFT 2 -> cj | |
| be AND bg -> bh | |
| lc LSHIFT 1 -> lw | |
| hm AND ho -> hp | |
| jr AND js -> ju | |
| 1 AND io -> ip | |
| cm AND co -> cp | |
| ib OR ic -> id | |
| NOT bf -> bg | |
| fo RSHIFT 5 -> fr | |
| ip LSHIFT 15 -> it | |
| jt AND jv -> jw | |
| jc AND je -> jf | |
| du OR dt -> dv | |
| NOT fx -> fy | |
| aw AND ay -> az | |
| ge LSHIFT 15 -> gi | |
| NOT ak -> al | |
| fm OR fn -> fo | |
| ff AND fh -> fi | |
| ci RSHIFT 5 -> cl | |
| cz OR cy -> da | |
| NOT ey -> ez | |
| NOT ju -> jv | |
| NOT ls -> lt | |
| kk AND kv -> kx | |
| NOT ii -> ij | |
| kl AND kr -> kt | |
| jk LSHIFT 15 -> jo | |
| e OR f -> g | |
| NOT bs -> bt | |
| hi AND hk -> hl | |
| hz OR ik -> il | |
| ek AND em -> en | |
| ao OR an -> ap | |
| dv LSHIFT 1 -> ep | |
| an LSHIFT 15 -> ar | |
| fo RSHIFT 1 -> gh | |
| NOT im -> in | |
| kk RSHIFT 1 -> ld | |
| hw LSHIFT 1 -> iq | |
| ec AND ee -> ef | |
| hb LSHIFT 1 -> hv | |
| kb AND kd -> ke | |
| x AND ai -> ak | |
| dd AND do -> dq | |
| aq OR ar -> as | |
| iq OR ip -> ir | |
| dl AND dn -> do | |
| iu RSHIFT 5 -> ix | |
| as OR bd -> be | |
| NOT go -> gp | |
| fk OR fj -> fl | |
| jm LSHIFT 1 -> kg | |
| NOT cv -> cw | |
| dp AND dr -> ds | |
| dt LSHIFT 15 -> dx | |
| et RSHIFT 1 -> fm | |
| dy RSHIFT 3 -> ea | |
| fp AND fv -> fx | |
| NOT p -> q | |
| dd RSHIFT 2 -> de | |
| eu AND fa -> fc | |
| ba AND bc -> bd | |
| dh AND dj -> dk | |
| lr AND lt -> lu | |
| he RSHIFT 1 -> hx | |
| ex AND ez -> fa | |
| df OR dg -> dh | |
| fj LSHIFT 15 -> fn | |
| NOT kx -> ky | |
| gk OR gq -> gr | |
| dy RSHIFT 2 -> dz | |
| gh OR gi -> gj | |
| lj AND ll -> lm | |
| x OR ai -> aj | |
| bz AND cb -> cc | |
| 1 AND lu -> lv | |
| as RSHIFT 3 -> au | |
| ce OR cd -> cf | |
| il AND in -> io | |
| dd RSHIFT 1 -> dw | |
| NOT lo -> lp | |
| c LSHIFT 1 -> t | |
| dd RSHIFT 3 -> df | |
| dd RSHIFT 5 -> dg | |
| lh AND li -> lk | |
| lf RSHIFT 5 -> li | |
| dy RSHIFT 5 -> eb | |
| NOT kt -> ku | |
| at OR az -> ba | |
| x RSHIFT 3 -> z | |
| NOT lk -> ll | |
| lb OR la -> lc | |
| 1 AND r -> s | |
| lh OR li -> lj | |
| ln AND lp -> lq | |
| kk RSHIFT 5 -> kn | |
| ea OR eb -> ec | |
| ci AND ct -> cv | |
| b RSHIFT 2 -> d | |
| jp RSHIFT 1 -> ki | |
| NOT cr -> cs | |
| NOT jd -> je | |
| jp RSHIFT 2 -> jq | |
| jn OR jo -> jp | |
| lf RSHIFT 3 -> lh | |
| 1 AND ds -> dt | |
| lf AND lq -> ls | |
| la LSHIFT 15 -> le | |
| NOT fg -> fh | |
| at AND az -> bb | |
| au AND av -> ax | |
| kw AND ky -> kz | |
| v OR w -> x | |
| kk OR kv -> kw | |
| ks AND ku -> kv | |
| kh LSHIFT 1 -> lb | |
| 1 AND kz -> la | |
| NOT kc -> kd | |
| x RSHIFT 2 -> y | |
| et OR fe -> ff | |
| et AND fe -> fg | |
| NOT ac -> ad | |
| jl OR jk -> jm | |
| 1 AND jj -> jk | |
| bn RSHIFT 1 -> cg | |
| NOT kp -> kq | |
| ci RSHIFT 3 -> ck | |
| ev AND ew -> ey | |
| 1 AND ke -> kf | |
| cj AND cp -> cr | |
| ir LSHIFT 1 -> jl | |
| NOT gw -> gx | |
| as RSHIFT 2 -> at | |
| iu RSHIFT 1 -> jn | |
| cy LSHIFT 15 -> dc | |
| hg OR hh -> hi | |
| ci RSHIFT 1 -> db | |
| au OR av -> aw | |
| km AND kn -> kp | |
| gj RSHIFT 1 -> hc | |
| iu RSHIFT 2 -> iv | |
| ab AND ad -> ae | |
| da LSHIFT 1 -> du | |
| NOT bw -> bx | |
| km OR kn -> ko | |
| ko AND kq -> kr | |
| bv AND bx -> by | |
| kl OR kr -> ks | |
| 1 AND ht -> hu | |
| df AND dg -> di | |
| NOT ag -> ah | |
| d OR j -> k | |
| d AND j -> l | |
| b AND n -> p | |
| gf OR ge -> gg | |
| gg LSHIFT 1 -> ha | |
| bn RSHIFT 5 -> bq | |
| bo OR bu -> bv | |
| 1 AND gy -> gz | |
| s LSHIFT 15 -> w | |
| NOT ie -> if | |
| as RSHIFT 5 -> av | |
| bo AND bu -> bw | |
| hz AND ik -> im | |
| bp AND bq -> bs | |
| b RSHIFT 1 -> v | |
| NOT l -> m | |
| bp OR bq -> br | |
| g AND i -> j | |
| br AND bt -> bu | |
| t OR s -> u | |
| hz RSHIFT 5 -> ic | |
| gk AND gq -> gs | |
| fl LSHIFT 1 -> gf | |
| he RSHIFT 3 -> hg | |
| gz LSHIFT 15 -> hd | |
| hf OR hl -> hm | |
| 1 AND gd -> ge | |
| fo OR fz -> ga | |
| id AND if -> ig | |
| fo AND fz -> gb | |
| gr AND gt -> gu | |
| he OR hp -> hq | |
| fq AND fr -> ft | |
| ga AND gc -> gd | |
| fo RSHIFT 2 -> fp | |
| gl OR gm -> gn | |
| hg AND hh -> hj | |
| NOT hn -> ho | |
| gl AND gm -> go | |
| he RSHIFT 5 -> hh | |
| NOT gb -> gc | |
| hq AND hs -> ht | |
| hz RSHIFT 3 -> ib | |
| hz RSHIFT 2 -> ia | |
| fq OR fr -> fs | |
| hx OR hy -> hz | |
| he AND hp -> hr | |
| gj RSHIFT 5 -> gm | |
| hf AND hl -> hn | |
| hv OR hu -> hw | |
| NOT hj -> hk | |
| gj RSHIFT 3 -> gl | |
| fo RSHIFT 3 -> fq | |
| he RSHIFT 2 -> hf |
Solution
Today's problem is quite difficult for me. But it only made me more challenged. At first, I was thinking of using VBA code to automate the whole things. But, running the code takes forever, maybe because I don't know how to break the loop. But, then I realize, that this puzzle can be done also with matching and sorting. So, in my Excel file below, I split the input into 5 parts: two variables, one operator, the-> and variable 3 (the result). 
=SUM(IF(B4="",1,0),IF(C4="",1,0),ISNUMBER(D4)))
This formula basically checks if the first variable and the operator is empty and the second is a number. Those meeting these conditions (signal in variable 3 is provided by variable 2) will give the sum of three. By sorting the columns (B-G) with value of G from largest to smallest, I can put those with numeric variable 2 in the top row. Then, I put this array formula in G6 (which has value less than 2):
=SUM(IF($B6="",1,0),IF($D6=$F$4:INDIRECT(ADDRESS(ROW(G$5),6)),1,0))+SUM(IF(ISNUMBER($B6),1,0),IF($D6=$F$4:INDIRECT(ADDRESS(ROW(G$5),6)),1,0))+SUM(IF(ISNUMBER($D6),1,0),IF($B6=$F$4:INDIRECT(ADDRESS(ROW(G$5),6)),1,0))
The formula again checks if any variable 1 and variable 2 matches those already declared variable 3 (
c and b respectively). Only if both match, or one variable match and another one is a number, that it will give values of one (true). Again, by sorting the columns (B-G) with value of G from largest to smallest, I can put those meeting the condition in the cells below the already declared variables. I repeat the process (with the help of a Macro) until the last row (G342). And, as I already guess, there is the desired output (signal provided to a) in the last row.
Now, to give value to variables 3, I made a custom function, called
Operate:Function Operate(a, b, c) As Double If c = "AND" Then Operate = WorksheetFunction.Bitand(a, b) ElseIf c = "OR" Then Operate = WorksheetFunction.Bitor(a, b) ElseIf c = "LSHIFT" Then Operate = WorksheetFunction.Bitlshift(a, b) ElseIf c = "RSHIFT" Then Operate = WorksheetFunction.Bitrshift(a, b) ElseIf c = "NOT" Then Operate = 65535 - b ElseIf c = "" Then Operate = b End If End Function
This function, basically put together all bitwise function needed (
BITAND, BITOR, BITLSHIFT, and BITRSHIFT), with addition of BITNOT (there is no such Excel function) and direct signal. Therefore, I just need to put this formula in column H:=Operate(IFERROR(INDEX($H$4:$H5,MATCH(B6,$F$4:$F$342,0)),B6),IFERROR(INDEX($H$4:$H5,MATCH(D6,$F$4:$F$342,0)),D6),C6)
The function IFERROR is needed because sometimes the variable (1 or 2) doesn't match with variable 3 and the formula returns an error value. The output is what I get in the last row.
Part 2
Description
Now, take the signal you got on wirea, override wire b to that signal, and reset the other wires (including wire a). What new signal is ultimately provided to wire a?Solution
For the part 2, I put the value ofb from the part 1 in the place of 44430 and calculate a using the same formula as above.
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