Cage Play 6: Killer 357 Multiples
(Published on 18. May 2025, 17:50 by HalfBakedLunatic)
The Rules:
• Normal Sudoku Rules Apply
• Cages sum to the number in the upper left corner, if given - digits can not repeat within a cage
• Each cage along a teal line must have digits that sum to a multiple of 3, 5, or 7 in rotating order (i.e., if a cage in the middle of a line is reduced to a multiple of 3 only, a cage on one side along the line must be a multiple of 5 and the cage on the other side must be a multiple of 7, and that sequence repeats. Any cage can be - and many times has to be - a multiple of two of these three numbers.)
Solve Online here (right-click and open in new tab):
Killer 357 Multiples (Cracking The Cryptic)
HINTS: (highlight hidden text to see it)
• No line can be a multiple of all three digits, and the smallest common denominator of 5 and 7 is 35, so cages that are 4 cells or less are restricted.
• The 357 sequence on bottom line that spans Row 8 can be determined. The 7 multiples are 'given' (from the 28 cage) so the rest must be either 3 or 5 multiples.
• The "Killer Calculator" in Sudokupad app can be invaluable here. With a cage that has no given total, you can 'red flag' or 'green flag' any cage sum, digit, or combination of digits. If a cage on one line is restricted to a multiple of 3, set all multiples of 3 to 'green' in the calculator. This may include 15 (which means that another line in the cage can be a 5 multiple), or 21 may allow a 7 multiple. If a cage has both 3 and 7 multiples, it can only be 21 or 42, for example.
• Determining whether the cages are 3 or 5 along the long top line (and the short lines in Box 5) is the most difficult. It will finally be resolved with the elbow shaped cage at R2C6, and then the correct sequences (and final digits) can be determined.
Leave a comment and let me know how you like it!
Puzzle by David Workman (aka "HalfBakedLunatic")
Solution code: Row 2
Comments
on 24. May 2025, 19:03 by skuntsel
A very nice puzzle! Quite hard to keep track of all options, and really easy to overlook a possible variant. But the flow is very smooth and the puzzle is very rewarding when you are attentive. I enjoyed it a lot! Keep the great puzzles coming!
-- Thank you skuntsel! Glad you enjoyed it :-)
on 22. May 2025, 03:30 by Criptonight
De toegevoegde aanwijzingen maakten een oplossing mogelijk, anders had ik het niet kunnen bereiken!
on 21. May 2025, 00:04 by Fool on Hill
The thing that helped me most was to colour along lines rather than colouring cages. Then I could see bi-colour cages more clearly and keep track of the line logic.. The hints are pretty much what I did to solve it.
-- Excellent! Changing from 'hidden' to 'normal' comment if you don't mind :-)
on 20. May 2025, 14:25 by BobAndWeave
I had a few false starts, but once I got going it was an amazing journey. Good 3 to 4 hours, but I was never completely stuck - just thinking through the logic. It's a brilliant, one of a kind puzzle!
-- Thanks Bob! Yeah, it a brain twister, that's for sure! Glad you liked it.
on 20. May 2025, 03:29 by HalfBakedLunatic
Adding hints to the puzzle description.
on 19. May 2025, 21:17 by Fool on Hill
Some really neat logic in there. Once I worked out a good method of keeping track of things it was easier to keep track of things. Enjoyed it - thanks for setting.
-- Thanks for the comments, it's always great hearing from you!
on 19. May 2025, 17:39 by PierreTombal
Beautiful logic. Quite tricky at first to keep track of the different factors but once I found a method that worked for me it had a great flow and the way the factors disambiguated was simply brilliant.
-- Thank you @PierreTombal! Very much appreciated. This was a tough one to construct, and even more challenging to test (as you mention, keeping track of everything is a challenge!)
