numc

Numc

Numc is a console C++ program that solves the Numbers round from the Letters and Numbers TV show. Given six integers and a target, it searches for expressions using each input at most once with +, -, *, and /. Division is integer-only (no remainder), and subtraction is only accepted when the result is non-negative. The program prints all unique solutions while accounting for commutativity and associativity, and it reports when none exist.

Example (Windows path shown; on macOS/Linux use ./numc):

x64/Release/numc.exe 100 75 25 10 7 5 666
...
1 259708 48 ((100+75+10)*(25-7)/5) = 666
2 3456920 12 ((((100-7)*(25+10))+75)/5) = 666
2 SOLUTIONS FOUND USING 6 NUMBERS, TESTED 30965760 CASES

Each solution line is <solution#> <case#> <hits> <expression> = <target>, where <case#> is the enumeration index at which the solution was first found and <hits> counts how many equivalent forms collapsed into it. A block of results is printed for every expression size from 1 to 6 numbers ("NO SOLUTIONS FOUND..." when a size has none). The search is deterministic integer arithmetic, so output is identical on all platforms.

Inputs are positional: six numbers followed by the target (7 args total). There is no argument validation, so always provide all seven values — fewer args crash.

Building and Running

Cross-platform since commit 32ad537: MSVC-only calls were replaced with portable ones (snprintf etc.), and a Makefile was added for non-Windows builds.

Windows (Visual Studio Community 2026 solution; MSVC + Windows SDK):

• Open numc.sln and build Release|x64 (or Debug|x64), or from a Developer Command Prompt:

msbuild numc.sln /p:Configuration=Release /p:Platform=x64
x64/Release/numc.exe 100 75 25 10 7 5 666

macOS/Linux (Apple clang or g++ both work):

make
./numc 100 75 25 10 7 5 666

The Windows binary under x64/Release/ is tracked in git; the Unix ./numc binary is gitignored and rebuilt locally.

GUI

numc.py is a Tkinter front end for the solver: enter the six numbers and the target (defaults 100 75 25 10 7 5 → 666), press [Calculate] or Enter, and the results appear in a scrollable text box. It validates all seven fields as 32-bit integers, then runs the solver on a background thread (10-minute timeout) with a live elapsed-time status line, so the window never freezes mid-search.

Run it with python numc.py (Windows) or python3 numc.py (macOS/Linux) after building the solver for your platform — it shells out to x64/Release/numc.exe on Windows and ./numc elsewhere, and shows a build hint if the binary is missing. It uses only the Python standard library (Homebrew Python on macOS may need brew install python-tk).

Desktop shortcuts

numc.ico (a red "666" calculator) is the icon used by the desktop shortcuts on both machines.

Windows: a regular desktop shortcut runs numc.py with numc.ico; the GUI also sets it as its window icon.

macOS (Mac mini): numc_launcher.applescript is the source for a small launcher app compiled with osacompile -o ~/Applications/Numc.app numc_launcher.applescript. Double-clicking it starts the GUI detached under /opt/homebrew/bin/python3; if the GUI is already running it brings the window to the front instead of starting a second copy (first use of that path asks a one-time Automation consent for System Events). The Desktop "Numc" shortcut is a Finder alias to that app. Notes for rebuilding it:

• The app lives in ~/Applications, not on the Desktop, to avoid macOS folder-access prompts; the script hardcodes this machine's repo path, so edit repoDir if the repo moves.
• Icon: convert numc.ico → .icns (sips → iconset → iconutil), copy it over Contents/Resources/applet.icns, then xattr -cr, codesign -f -s -, and set the Finder icon via NSWorkspace setIcon:forFile: last (that order matters — xattr -cr/codesign strip or reject a pasted-on icon).
• On an iCloud-synced Desktop the alias itself must also get the icon pasted on (plus SetFile -a C to force the custom-icon flag), or it renders generic — and iCloud strips it again after launches. The "Refresh Icons" tool in the Claude_Python_Testbed repo (desktop_launchers/refresh_launcher_icons.command) re-applies all launcher icons including Numc's; its master image icon_numc_master.png lives there.

Structure and Logic

All solver code lives in numc.cpp (~700 lines) — it is the only translation unit in the build (both numc.vcxproj and the Makefile compile just this file). numc.h is an empty placeholder. numd.cpp is a stale near-duplicate that is not part of the build; make changes in numc.cpp only. Visual Studio artifacts are numc.sln, numc.vcxproj, and numc.vcxproj.filters; numc.py, numc.ico, and numc_launcher.applescript are the GUI/launcher layer described above.

Search enumeration

main() reads the six numbers into av[6] and the target into ag, then runs one block per expression size: CheckBlock1() handles the trivial one-number case, and five CheckBlock(xn, xk, xm, xq, xcn, xci, xt) calls handle sizes 2–6 with hard-coded parameters per size (operator count, bracketing-table slice, template trim). Each block brute-forces the cross product of:

• permutations of the input numbers (GenerateNextPermutation, stepping the global a[]),
• operator combinations over + - * / (GenerateNextCombination, stepping b[]) — 4^(k-1) combos for k numbers,
• bracketing shapes from the c[42][12] table — the slice used per size has 1, 2, 5, 14, 42 rows for 2–6 numbers (the Catalan numbers, i.e. every distinct way to parenthesize).

So the 6-number block tests 720 × 4^5 × 42 = 30,965,760 cases, matching the count the program prints; the 5-number block's 2,580,480 likewise.

Each c[42][12] row is a postfix (RPN) template string: 'a' means "push the next number of the current permutation" and a digit means "apply operator b[digit - ci]", where ci trims the template for smaller expression sizes. Treat the table as a fixed constant — the CheckBlock parameters assume its exact layout.

Evaluation

TryPermCombBracTriplet() evaluates the current template on a fixed int stack (si[]), applying Op() for each operator. Op() enforces the game rules: division must be exact, subtraction must not go negative, and any invalid intermediate result becomes the sentinel ERINT = -6666, which poisons everything downstream so the case is rejected.

Canonicalization and deduplication

On a target match, CreateSortedExpressionString_Enhanced() builds a canonical string so algebraically equivalent expressions collapse to one solution: it flattens chains of +/- and *// into term lists, sorts the terms by signed value with a string hash (strHash) as tie-break, and re-parenthesizes. This canonicalization is the subtle part of the codebase — most deduplication bugs live here. Unique strings are stored in fs[5000][40] with hit counters and discovery indices in the parallel fsn[]/fsi1[]/fsii[] arrays (hard caps, no bounds checks), and each block prints its stored solutions at the end.

Global state

Functions communicate through fixed-size globals rather than parameters, and there is no dynamic allocation anywhere (keep it that way — see AGENTS.md): av[]/ag are the inputs, a[]/b[] the current permutation/operator combo, br[]/si[]/so[]/ssp[] the expression-building stacks, sbr[][]/ssi[][]/sso[][] etc. the parallel stacks used during canonical string construction (index TMP = 6 is the scratch slot), and fs[] and friends the solution store.

Contributor Docs

• AGENTS.md — repository guidelines (style, build, testing conventions).
• CLAUDE.md — orientation for Claude Code sessions working in this repo.