Medium 6×6 cage-sum puzzle #29.

Puzzle signature

Medium profile: 12 cages · 7 distinct cage totals · target range 6–16 · 3 two-cell cages · logic score 115. Use this profile as a quick map of the board's strongest cage constraints before you replay the round.

Puzzle analysis

This PUZRU archive puzzle uses 12 connected sum cages across a 6×6 grid with 6 carried fixed values. Its cage profile contains 3 two-cell, 6 three-cell and 3 four-cell cages. Target sums range from 6 to 16, with an average cage target of 10.5.

The generator assigned a logic score of 115, which PUZRU classifies as Medium. The archived quality record verifies one exact solution and a logical solve path without random guessing.

What makes this round distinct

This board combines 7 distinct cage totals. It contains 0 low-target cages (5 or below) and 0 high-target cages (18 or above), creating a round-specific balance between constrained low combinations and high-digit pressure. Its 3 two-cell cages create especially short candidate lists that interact tightly with row and column exclusions.

Logical deduction trace

1. R1C5 starts fixed at 6 from the Chain carry.
2. R2C1 starts fixed at 3 from the Chain carry.
3. R3C4 starts fixed at 6 from the Chain carry.
4. R4C6 starts fixed at 2 from the Chain carry.
5. R5C3 starts fixed at 6 from the Chain carry.
6. R6C2 starts fixed at 5 from the Chain carry.
7. Cage R3C3, R3C4, R3C5 totals 14; this removes 1/2/4 from R3C3.
8. Cage R3C3, R3C4, R3C5 totals 14; this removes 1/2/4 from R3C5.
9. Cage R4C5, R5C5 totals 6; this removes 3 from R4C5.
10. Cage R4C5, R5C5 totals 6; this removes 3/4 from R5C5.
11. Cage R2C5, R2C6, R3C6 totals 8; this removes 5 from R2C5.
12. Cage R2C5, R2C6, R3C6 totals 8; this removes 4 from R3C6.
13. Cage R4C6, R5C6, R6C6 totals 11; this removes 1/4 from R5C6.
14. Cage R4C6, R5C6, R6C6 totals 11; this removes 1/3 from R6C6.
15. Cage R6C1, R6C2 totals 6; this removes 2/4/6 from R6C1.
16. Cage R2C2, R3C2 totals 8; this removes 1/2/4 from R2C2.
17. Cage R2C2, R3C2 totals 8; this removes 1/3/4 from R3C2.
18. Cage R5C4, R6C4, R6C5 totals 9; this removes 1 from R5C4.
19. R2C2 has only candidate 6 after row, column and cage elimination. Set R2C2 = 6.
20. Row 3 can place 4 only at R3C1. Set R3C1 = 4.
21. R3C2 has only candidate 2 after row, column and cage elimination. Set R3C2 = 2.
22. Column 1 can place 6 only at R4C1. Set R4C1 = 6.
23. R6C1 has only candidate 1 after row, column and cage elimination. Set R6C1 = 1.
24. Row 6 can place 6 only at R6C6. Set R6C6 = 6.

How to approach this 6×6 puzzle

• After every cage deduction, scan both the row and the column before committing a value. PUZRU puzzles are designed so cage arithmetic and Latin-square constraints reinforce each other.

The live result

ARNATUILE became the Discoverer by submitting the first verified solution accepted by the global authority. After that moment, the shared 45-second contribution window remained open and the puzzle finished with 1 verified solver.

Six values continued into the Chain

The PUZRU world never resets to a completely unrelated board. Six solved positions from this puzzle were carried into the next puzzle as fixed values. For Puzzle #29, the carried values were 4 1 4 1 6 4.

This carry rule makes every puzzle both a standalone logic challenge and one link in an ongoing global sequence.

Chain proof

The public archive records the completed puzzle and its cryptographic Chain hash so later rounds can be linked back to the same history.

SoePzu5924BUW9bdiwkGZ2cBTSNRCfoGTBFFiAac23o

Archive replay is unranked: it never changes the live Chain or leaderboard.

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