The Chamber of Duplicates

Find the only orderly code of 6 digits.

Materials: Pencil, gum and gridded paper; no commercial game required.

Rules you need

Each position contains a number from 0 to 7. Repeats are allowed. The code has exactly 6 positions; an initial zero is allowed.
"Good place" includes the positions whose number and place are correct. "Unplaced" counts the other numbers present, respecting the multiplicity.
To count the wrong placed, first matches the well placed numbers, then each remaining occurrence at the most once. The indices do not give the location of the incorrectly placed numbers.
All indices are simultaneously true. There is no hidden information about colors, parity or missing numbers.

The puzzle

The table reads from top to bottom. The proposals are tests and are not already confirmed number positions.

Write down the possible multiplicities of each number, then look for arrangements compatible with all scores.

Coordinates: lines from top to bottom, columns from left to right.
L / C	1	2	3	4
1	Test	Guess	Exact matches	Misplaced matches
2	1	474563	1	2
3	2	013237	1	3
4	3	163003	2	3
5	4	635050	0	3
6	5	042546	1	2

Why this level?

The reference method leaves 1 multiset(s) after solving multiplicity constraints; then it is necessary to cross their arrangements with all position constraints. The resolution combines equations of multiplicity ceilings, permutations with repetition and intertwined position constraints. The corrected provides the complete cutting of this exploration. The Extreme level remains an appreciation of this manual effort, without calibration on players.

Your workspace

Write down your assumptions separately from deductions you have proved.

Notes for SOLO-014

View the solution to SOLO-014 →