Counterfeit Coin
(Published on 29. September 2024, 21:29 by vitaminz)
I ended up making two versions of this puzzle. The pictured version I think is slightly easier to execute on despite having fewer clues, but I think the harder version
(click here to play) actually slightly better telegraphs the opening idea. Feel free to try either puzzle - though they have different solutions, the section for the solution code is the same. Please leave a comment if you enjoy it!
RULES:
Normal Sudoku Rules Apply
1/9 Column Indexing: The digit in row X of column (1/9) indicates the position of (1/9) in row X.
Killer Cages: Digits in a killer cage sum to the total in the top-left corner of the cage.
Balancers: You have a bag of 9 coins which each bear a digit from 1-9. All of these coins weigh exactly the same weight, except for one which is a counterfeit, and is lighter or heavier (to be deduced) than the others.
You find the counterfeit coin in a series of weighings. Each weighing has 3 coins on each side, and the results are shown. Each time, the lower side indicates that the 3 coins on that side have a combined weight greater than those on the other side.
Each weighing groups coins by one of three properties: entropy, polarity, or residue mod 3. Each property is used in one of the weighings.
The coins on one side will all share a property and differ from the coins on the other side with regards to the same property.
Full property descriptions:
Entropy: 1,2,3 vs. 4,5,6 vs. 7,8,9.
Residue class (mod 3): 1,4,7, vs. 2,5,8. vs. 3,6,9.
Parity: 1,3,5,7,9 vs. 2,4,6,8.
Example: if the weighing is grouping by entropy then the coins on one side might be 456 and the coins on the other side might be 123.
RULES:
Normal Sudoku Rules Apply
1/9 Column Indexing: The digit in row X of column (1/9) indicates the position of (1/9) in row X.
Killer Cages: Digits in a killer cage sum to the total in the top-left corner of the cage.
Balancers: You have a bag of 9 coins which each bear a digit from 1-9. All of these coins weigh exactly the same weight, except for one which is a counterfeit, and is lighter or heavier (to be deduced) than the others.
You find the counterfeit coin in a series of weighings. Each weighing has 3 coins on each side, and the results are shown. Each time, the lower side indicates that the 3 coins on that side have a combined weight greater than those on the other side.
Each weighing groups coins by one of three properties: entropy, polarity, or residue mod 3. Each property is used in one of the weighings.
The coins on one side will all share a property and differ from the coins on the other side with regards to the same property.
Full property descriptions:
Entropy: 1,2,3 vs. 4,5,6 vs. 7,8,9.
Residue class (mod 3): 1,4,7, vs. 2,5,8. vs. 3,6,9.
Parity: 1,3,5,7,9 vs. 2,4,6,8.
Example: if the weighing is grouping by entropy then the coins on one side might be 456 and the coins on the other side might be 123.
Solution code: The first 6 digits of box 9, in reading order.
Last changed on on 30. September 2024, 04:13
Solved by SKORP17, Gilliatt, Sotehr, ViKingPrime, roflsalot, karlmortenlunna, marty_sears, Snookerfan, palpot, lmdemasi, ThePedallingPianist, Ratfinkz, LehanLehan, Nell Gwyn, fkib, PippoForte, QuiltyAsCharged
Comments
on 7. August 2025, 23:09 by QuiltyAsCharged
An excellent and wonderfully crafted puzzle
on 19. October 2024, 09:41 by LehanLehan
Really unusual idea,great puzzle, Justin
on 30. September 2024, 12:38 by Snookerfan
Great puzzle! I solved the harder one for the challenge. When the penny finally dropped, it became very smooth. Thank you
on 30. September 2024, 02:37 by ViKingPrime
This was beautifully conceived and beautifully executed.
