gchq/CyberChef · error · OperationError

Χ3 start must be between 1 and 29

Error message

Χ3 start must be between 1 and 29

What it means

Colossus simulates the Lorenz SZ cipher; the chi-3 (Χ3) wheel has exactly 29 cam positions. The start position is a 1-based index, enforced by `if (args[47]<1 || args[47]>29)`. Any value outside [1, 29] is rejected before the simulation runs.

Source

Thrown at src/core/operations/Colossus.mjs:442

            throw new OperationError("Set Total must be between 0000 and 9999");

        // null|fast|slow for each of S1-5,M1-2,X1-5
        const control = {
            fast: args[43],
            slow: args[44]
        };

        // Start positions
        if (args[52]<1 || args[52]>43) throw new OperationError("Ψ1 start must be between 1 and 43");
        if (args[53]<1 || args[53]>47) throw new OperationError("Ψ2 start must be between 1 and 47");
        if (args[54]<1 || args[54]>51) throw new OperationError("Ψ3 start must be between 1 and 51");
        if (args[55]<1 || args[55]>53) throw new OperationError("Ψ4 start must be between 1 and 53");
        if (args[56]<1 || args[57]>59) throw new OperationError("Ψ5 start must be between 1 and 59");
        if (args[51]<1 || args[51]>37) throw new OperationError("Μ37 start must be between 1 and 37");
        if (args[50]<1 || args[50]>61) throw new OperationError("Μ61 start must be between 1 and 61");
        if (args[45]<1 || args[45]>41) throw new OperationError("Χ1 start must be between 1 and 41");
        if (args[46]<1 || args[46]>31) throw new OperationError("Χ2 start must be between 1 and 31");
        if (args[47]<1 || args[47]>29) throw new OperationError("Χ3 start must be between 1 and 29");
        if (args[48]<1 || args[48]>26) throw new OperationError("Χ4 start must be between 1 and 26");
        if (args[49]<1 || args[49]>23) throw new OperationError("Χ5 start must be between 1 and 23");

        const starts = {
            X1: args[45], X2: args[46], X3: args[47], X4: args[48], X5: args[49],
            M61: args[50], M37: args[51],
            S1: args[52], S2: args[53], S3: args[54], S4: args[55], S5: args[56]
        };

        const colossus = new ColossusComputer(input, pattern, qbusin, qbusswitches, control, starts, settotal, limit);
        const result = colossus.run();

        return result;
    }

    /**
     * Select Program
     *

View on GitHub (pinned to 4290ea7539)

Solutions

1. Set the Χ3 start argument to an integer in the inclusive range [1, 29].
2. Verify the value against the Lorenz SZ chi-3 wheel length of 29.
3. Validate all start positions programmatically against their per-wheel maximums before baking.

Example fix

// before
args[47] = 30; // throws: Χ3 start must be between 1 and 29
// after
args[47] = 29; // valid: chi-3 wheel has 29 positions

const CHI3_START_MAX = 29;
function validChi3Start(v) {
  return Number.isInteger(v) && v >= 1 && v <= CHI3_START_MAX;
}
if (!validChi3Start(starts.X3)) {
  throw new Error(`Χ3 start ${starts.X3} out of range [1, ${CHI3_START_MAX}]`);
}

function isChi3Start(v) {
  return Number.isInteger(v) && v >= 1 && v <= 29;
}

When it happens

Trigger: Setting the 'Χ3 start' argument (args[47]) to 0, a negative number, or an integer greater than 29. Also when a transcribed key setting uses the wrong wheel length for chi-3.

Common situations: Off-by-one (0-based assumption); mistaking Χ3's length (29) for another wheel's; bulk-pasting a start vector where columns are misaligned.

Related errors

• Χ2 start must be between 1 and 31
• Χ4 start must be between 1 and 26
• Error opening image. (${err})
• Unsupported QR code format.
• Unknown padding type: ${padding}

AI-assisted analysis of gchq/CyberChef@4290ea7539 (2026-08-13). Data as JSON: /api/errors/309bbe7bf29d081a. Report an issue: GitHub.