exercism · depial · Dec 6, 2025 · Dec 6, 2025 · Dec 6, 2025
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
@@ -95,7 +95,7 @@ After following the steps above, your exercise should contain _at least_ the fol
 
 Further, an entry in `config.json` was added for the exercise.
 
-It may contain further files, e.g. to add additional information or provide extra code. This is the bare minimum.
+It may contain further files, e.g. to add additional information or provide extra code. This is the bare minimum. See `README.md` for further formatting standards.
 
 Take a look at the `exercise/` directory or commit history for examples, or at this [example](https://github.com/exercism/julia/pull/560) of what a PR adding a new exercise should look like.
 

diff --git a/README.md b/README.md
@@ -101,7 +101,7 @@ Likewise, `.meta/example.jl` or `.meta/exemplar.jl` does not need to `import`/`i
 
 ### config.json
 If helper files are needed, `.meta/config.json` should then take an entry under the `"files"` property.
-1. If the file is meant to be visible to the student, use `editor`:
+1. If the file is meant to be visible to the student (e.g. [Alphametics](https://github.com/exercism/julia/tree/main/exercises/practice/alphametics)), use `editor`:
 
 ```json
   "files": {

diff --git a/exercises/practice/alphametics/.docs/instructions.append.md b/exercises/practice/alphametics/.docs/instructions.append.md
@@ -1,3 +1,6 @@
 # Instructions append
 
 You may (or may not!) want to call the function `permutations(a, t)` from [Combinatorics.jl](https://github.com/JuliaMath/Combinatorics.jl) in your solution.
+
+- If working either in the online editor or locally with `Combinatorics.jl` installed in your environment, `permutations(a, t)` is already in the namespace, but you would normally need to add one of: `using Combinatorics` or `using Combinatorics: permutations` to your solution file.
+- If working locally, without `Combinatorics.jl` installed in your environment, you can uncomment the relevant code in `permutations.jl` and add `include("permutations.jl")` at the top of your solution file to access `permutations(a, t)`. You will also need to comment out or remove the line `using Combinatorics: permutations` in `runtests.jl`.
diff --git a/exercises/practice/alphametics/.meta/config.json b/exercises/practice/alphametics/.meta/config.json
@@ -12,6 +12,9 @@
     ],
     "example": [
       ".meta/example.jl"
+    ],
+    "editor": [
+      "permutations.jl"
     ]
   },
   "blurb": "Given an alphametics puzzle, find the correct solution."

diff --git a/exercises/practice/alphametics/.meta/example.jl b/exercises/practice/alphametics/.meta/example.jl
@@ -1,104 +1,53 @@
-### Simple helper functions
-
-"""
-    leading_letters(puzzle)
-
-Return each unique character that leads a word in the puzzle.
-"""
-function leading_letters(puzzle)
-    unique(first.(split(puzzle, r"[^A-Z]+")))
-end
-
-"""
-    letters(puzzle)
-
-Return the unique letters in the puzzle in a deterministic order.
-"""
-letters(puzzle) = unique(c for c in puzzle if c in 'A':'Z')
-
-
-### British Informatics Olympiad inspired brute-force solution
-
-"""
-    parse_puzzle(puzzle)
-
-An alphametic puzzle like "A + A + B == AA" can be represented as an equation
-and a list of letters used as leading digits. The equation looks like this:
-
-    A + A + B == 10A + A
-
-We can rearrange and simplify that to a set of coefficients:
-
-    2A + B == 11A
-    -9A + B == 0
-
-This function returns three vectors:
-
-- the unique letters of the puzzle in the order that they are used in the next
-  two vectors
-- coefficients for each letter
-- a boolean vector indicating if the letter is ever used as a leading digit
-
-"""
-function parse_puzzle(puzzle::String)
-    key = letters(puzzle)
-    lhs = zeros(Int, length(key))
-    rhs = zeros(Int, length(key))
-    acc = lhs
-    for token in split(puzzle)
-        if token == "=="
-            acc = rhs
-        elseif token != "+"
-            parse_word!(acc, key, token)
-        end
-    end
-    coeffs = lhs .- rhs
-    return key, coeffs, map(∈(leading_letters(puzzle)), key)
-end
-
-"""
-    parse_word!(acc, key, word)
-
-`acc` is a vector of coefficients to apply to the variables in `key`.
-`word` is a string representing more coefficients for those variables.
-
-Update `acc` by adding these coefficients together.
-
-"""
-function parse_word!(acc, key, word)
-    multiplier = 10 ^ (length(word) - 1)
-    for l in word
-        acc[findfirst(==(l), key)] += multiplier
-        multiplier ÷= 10
-    end
-    acc
-end
-
-"""
-    is_valid(p, coeffs, leads)
-
-Return true iff `sum(p .* coeffs) == 0` and no leading digit is 0.
-"""
-function is_valid(p, coeffs, leads)
-    # Using generators + zip leads to many fewer allocations than .*
-    sum(p_i * coeffs_i for (p_i, coeffs_i) in zip(p, coeffs)) == 0 &&
-    all(p[l_i] != 0 for (l_i, l) in enumerate(leads) if l)
-end
-
-"""
-    solve(puzzle::String)
-
-Return a Dict mapping each letter in the puzzle to an integer in 0:9.
-
-Words cannot start with 0.
-No two letters can share the same value.
-"""
 function solve(puzzle)
-    (key, coeffs, leads) = parse_puzzle(puzzle)
-    for p in permutations(0:9, length(key))
-        if is_valid(p, coeffs, leads)
-            return Dict(key .=> p)
-        end
+    terms = reverse.(split(replace(puzzle, r"[+=]"=> ""), "  "))
+    leading = Set(last.(terms))
+    addends, result = terms[1:end-1], last(terms)
+    solution, maxdigits = Dict(), maximum(length, addends)
+
+    function prunedfs(term=1, digit=1, colsum=0)
+        if term ≤ length(addends) && digit ≤ length(addends[term])
+            if haskey(solution, addends[term][digit])
+                return prunedfs(term+1, digit, colsum + solution[addends[term][digit]])
+            else
+                for i in 0:9
+                    iszero(i) && addends[term][digit] ∈ leading && continue
+                    if i ∉ values(solution)
+                        solution[addends[term][digit]] = i
+                        check = prunedfs(term+1, digit, colsum + solution[addends[term][digit]])
+                        isnothing(check) ? (delete!(solution, addends[term][digit]); nothing) : return check
+                    end
+                end
+            end
+        elseif term ≤ length(addends)
+            return prunedfs(term+1, digit, colsum)
+        else
+            if digit < maxdigits
+                if result[digit] ∈ leading && iszero(colsum%10)
+                    nothing
+                elseif haskey(solution, result[digit]) && solution[result[digit]] == colsum%10
+                    return prunedfs(1, digit+1, colsum÷10)
+                elseif !haskey(solution, result[digit]) && colsum%10 ∉ values(solution)
+                    solution[result[digit]] = colsum%10
+                    check = prunedfs(1, digit+1, colsum÷10)
+                    isnothing(check) ? (delete!(solution, result[digit]); nothing) : return check
+                end
+            else
+                check, added, total = [], [], digits(colsum)
+                if length(total) == length(result[digit:end])
+                    for (i, ch) in enumerate(result[digit:end])
+                        !haskey(solution, ch) && total[i] ∈ values(solution) && break
+                        ch ∈ leading && iszero(total[i]) && break
+                        if !haskey(solution, ch) && total[i] ∉ values(solution)
+                            solution[ch] = total[i]
+                            push!(added, ch)
+                        end
+                        push!(check, solution[ch]) 
+                    end
+                check != total ? foreach(ch-> delete!(solution, ch), added) : return solution
+                end
+            end
+        end                     
     end
-    return nothing
+
+    prunedfs()
 end
diff --git a/exercises/practice/alphametics/permutations.jl b/exercises/practice/alphametics/permutations.jl
@@ -0,0 +1,115 @@
+# Extract of Combinatorics.jl
+#
+# You may (or may not!) want to call the function `permutations(a, t)` in your
+# solution.
+#
+# License:
+#
+#    Copyright (c) 2013-2015: Alessandro Andrioni, Jiahao Chen and other
+#    contributors.
+#
+#    Permission is hereby granted, free of charge, to any person obtaining a
+#    copy of this software and associated documentation files (the "Software"),
+#    to deal in the Software without restriction, including without limitation
+#    the rights to use, copy, modify, merge, publish, distribute, sublicense,
+#    and/or sell copies of the Software, and to permit persons to whom the
+#    Software is furnished to do so, subject to the following conditions:
+#
+#    The above copyright notice and this permission notice shall be included in
+#    all copies or substantial portions of the Software.
+#
+#    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+#    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+#    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+#    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+#    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+#    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+#    DEALINGS IN THE SOFTWARE.
+
+# Combinatorics/src/factorials.jl
+
+# TODO: Uncomment below for use locally (not available for web editor)
+
+# """
+#     factorial(n, k)
+# Compute ``n!/k!``.
+# """
+# function Base.factorial(n::T, k::T) where T<:Integer
+#     if k < 0 || n < 0 || k > n
+#         throw(DomainError((n, k), "n and k must be nonnegative with k ≤ n"))
+#     end
+#     f = one(T)
+#     while n > k
+#         f = Base.checked_mul(f, n)
+#         n -= 1
+#     end
+#     return f
+# end
+
+# Base.factorial(n::Integer, k::Integer) = factorial(promote(n, k)...)
+
+# # Combinatorics/src/permutations.jl
+
+# struct Permutations{T}
+#     a::T
+#     t::Int
+# end
+
+# Base.eltype(::Type{Permutations{T}}) where {T} = Vector{eltype(T)}
+
+# Base.length(p::Permutations) = (0 <= p.t <= length(p.a)) ? factorial(length(p.a), length(p.a)-p.t) : 0
+
+# """
+#     permutations(a)
+# Generate all permutations of an indexable object `a` in lexicographic order. Because the number of permutations
+# can be very large, this function returns an iterator object.
+# Use `collect(permutations(a))` to get an array of all permutations.
+# """
+# permutations(a) = Permutations(a, length(a))
+
+# """
+#     permutations(a, t)
+# Generate all size `t` permutations of an indexable object `a`.
+# """
+# function permutations(a, t::Integer)
+#     if t < 0
+#         t = length(a) + 1
+#     end
+#     Permutations(a, t)
+# end
+
+# function Base.iterate(p::Permutations, s = collect(1:length(p.a)))
+#     (!isempty(s) && max(s[1], p.t) > length(p.a) || (isempty(s) && p.t > 0)) && return
+#     nextpermutation(p.a, p.t ,s)
+# end
+
+# function nextpermutation(m, t, state)
+#     perm = [m[state[i]] for i in 1:t]
+#     n = length(state)
+#     if t <= 0
+#         return(perm, [n+1])
+#     end
+#     s = copy(state)
+#     if t < n
+#         j = t + 1
+#         while j <= n &&  s[t] >= s[j]; j+=1; end
+#     end
+#     if t < n && j <= n
+#         s[t], s[j] = s[j], s[t]
+#     else
+#         if t < n
+#             reverse!(s, t+1)
+#         end
+#         i = t - 1
+#         while i>=1 && s[i] >= s[i+1]; i -= 1; end
+#         if i > 0
+#             j = n
+#             while j>i && s[i] >= s[j]; j -= 1; end
+#             s[i], s[j] = s[j], s[i]
+#             reverse!(s, i+1)
+#         else
+#             s[1] = n+1
+#         end
+#     end
+#     return (perm, s)
+# end
diff --git a/exercises/practice/alphametics/runtests.jl b/exercises/practice/alphametics/runtests.jl
@@ -1,4 +1,5 @@
-using Test, Combinatorics
+using Test
+using Combinatorics: permutations # comment out or remove if Combinatorics.jl is not installed
 
 include("alphametics.jl")
 
@@ -72,33 +73,35 @@ include("alphametics.jl")
         )
     end
 
-    @testset "puzzle with ten letters" begin
-        @test solve("AND + A + STRONG + OFFENSE + AS + A + GOOD == DEFENSE") == Dict(
-            'A' => 5,
-            'D' => 3,
-            'E' => 4,
-            'F' => 7,
-            'G' => 8,
-            'N' => 0,
-            'O' => 2,
-            'R' => 1,
-            'S' => 6,
-            'T' => 9
-        )
-    end
+    # TODO: Combinatorics.jl is currently too slow for the following tests
+
+    # @testset "puzzle with ten letters" begin
+    #     @test solve("AND + A + STRONG + OFFENSE + AS + A + GOOD == DEFENSE") == Dict(
+    #         'A' => 5,
+    #         'D' => 3,
+    #         'E' => 4,
+    #         'F' => 7,
+    #         'G' => 8,
+    #         'N' => 0,
+    #         'O' => 2,
+    #         'R' => 1,
+    #         'S' => 6,
+    #         'T' => 9
+    #     )
+    # end
 
-    @testset "puzzle with ten letters and 199 addends" begin
-        @test solve("THIS + A + FIRE + THEREFORE + FOR + ALL + HISTORIES + I + TELL + A + TALE + THAT + FALSIFIES + ITS + TITLE + TIS + A + LIE + THE + TALE + OF + THE + LAST + FIRE + HORSES + LATE + AFTER + THE + FIRST + FATHERS + FORESEE + THE + HORRORS + THE + LAST + FREE + TROLL + TERRIFIES + THE + HORSES + OF + FIRE + THE + TROLL + RESTS + AT + THE + HOLE + OF + LOSSES + IT + IS + THERE + THAT + SHE + STORES + ROLES + OF + LEATHERS + AFTER + SHE + SATISFIES + HER + HATE + OFF + THOSE + FEARS + A + TASTE + RISES + AS + SHE + HEARS + THE + LEAST + FAR + HORSE + THOSE + FAST + HORSES + THAT + FIRST + HEAR + THE + TROLL + FLEE + OFF + TO + THE + FOREST + THE + HORSES + THAT + ALERTS + RAISE + THE + STARES + OF + THE + OTHERS + AS + THE + TROLL + ASSAILS + AT + THE + TOTAL + SHIFT + HER + TEETH + TEAR + HOOF + OFF + TORSO + AS + THE + LAST + HORSE + FORFEITS + ITS + LIFE + THE + FIRST + FATHERS + HEAR + OF + THE + HORRORS + THEIR + FEARS + THAT + THE + FIRES + FOR + THEIR + FEASTS + ARREST + AS + THE + FIRST + FATHERS + RESETTLE + THE + LAST + OF + THE + FIRE + HORSES + THE + LAST + TROLL + HARASSES + THE + FOREST + HEART + FREE + AT + LAST + OF + THE + LAST + TROLL + ALL + OFFER + THEIR + FIRE + HEAT + TO + THE + ASSISTERS + FAR + OFF + THE + TROLL + FASTS + ITS + LIFE + SHORTER + AS + STARS + RISE + THE + HORSES + REST + SAFE + AFTER + ALL + SHARE + HOT + FISH + AS + THEIR + AFFILIATES + TAILOR + A + ROOFS + FOR + THEIR + SAFE == FORTRESSES") == Dict(
-            'A' => 1,
-            'E' => 0,
-            'F' => 5,
-            'H' => 8,
-            'I' => 7,
-            'L' => 2,
-            'O' => 6,
-            'R' => 3,
-            'S' => 4,
-            'T' => 9
-        )
-    end
+    # @testset "puzzle with ten letters and 199 addends" begin
+    #     @test solve("THIS + A + FIRE + THEREFORE + FOR + ALL + HISTORIES + I + TELL + A + TALE + THAT + FALSIFIES + ITS + TITLE + TIS + A + LIE + THE + TALE + OF + THE + LAST + FIRE + HORSES + LATE + AFTER + THE + FIRST + FATHERS + FORESEE + THE + HORRORS + THE + LAST + FREE + TROLL + TERRIFIES + THE + HORSES + OF + FIRE + THE + TROLL + RESTS + AT + THE + HOLE + OF + LOSSES + IT + IS + THERE + THAT + SHE + STORES + ROLES + OF + LEATHERS + AFTER + SHE + SATISFIES + HER + HATE + OFF + THOSE + FEARS + A + TASTE + RISES + AS + SHE + HEARS + THE + LEAST + FAR + HORSE + THOSE + FAST + HORSES + THAT + FIRST + HEAR + THE + TROLL + FLEE + OFF + TO + THE + FOREST + THE + HORSES + THAT + ALERTS + RAISE + THE + STARES + OF + THE + OTHERS + AS + THE + TROLL + ASSAILS + AT + THE + TOTAL + SHIFT + HER + TEETH + TEAR + HOOF + OFF + TORSO + AS + THE + LAST + HORSE + FORFEITS + ITS + LIFE + THE + FIRST + FATHERS + HEAR + OF + THE + HORRORS + THEIR + FEARS + THAT + THE + FIRES + FOR + THEIR + FEASTS + ARREST + AS + THE + FIRST + FATHERS + RESETTLE + THE + LAST + OF + THE + FIRE + HORSES + THE + LAST + TROLL + HARASSES + THE + FOREST + HEART + FREE + AT + LAST + OF + THE + LAST + TROLL + ALL + OFFER + THEIR + FIRE + HEAT + TO + THE + ASSISTERS + FAR + OFF + THE + TROLL + FASTS + ITS + LIFE + SHORTER + AS + STARS + RISE + THE + HORSES + REST + SAFE + AFTER + ALL + SHARE + HOT + FISH + AS + THEIR + AFFILIATES + TAILOR + A + ROOFS + FOR + THEIR + SAFE == FORTRESSES") == Dict(
+    #         'A' => 1,
+    #         'E' => 0,
+    #         'F' => 5,
+    #         'H' => 8,
+    #         'I' => 7,
+    #         'L' => 2,
+    #         'O' => 6,
+    #         'R' => 3,
+    #         'S' => 4,
+    #         'T' => 9
+    #     )
+    # end
 end