Fanning a Sudoku Spark into a Flame!
ฝัง
- เผยแพร่เมื่อ 12 ก.ย. 2024
- BremSter solves "Diamond In The Rough" by fjam. An Sudoku using the Sum Lines and Ratio Pairs constraints.
Solve in Sven's SudokuPad WebApp: sudokupad.app/...
📋 Puzzle Rules:
• Normal Sudoku rules apply.
• Along each blue line, digits in each region must sum to the same total. If a line has multiple disconnected segments within a region, these segments are summed separately.
• Cells separated by a black dot must contain digits with a ratio of 1:2. Not all dots are given.
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Really nicely done Bremster! There are a few ways to tackle the diamond, which I like as it means that solvers should be able to find some way to get started. Recognising the sum has to be even and then eliminating options is a good choice, as is the trick with divisibility by 5. Neither is right or wrong, what matters to me is that solvers explore and come to understand the pattern one way or another. I wanted the rest of the puzzle to be pretty smooth afterwards, just asking simple questions. I was pleased to be able to find a layout that is completely symmetric apart from box 5, but I also wanted that symmetry to be broken early so I avoided making a puzzle where every cell was a pair for ages (not really my style).
I enjoyed the singing too, which I hope was the sign of somebody feeling relaxed and enjoying themselves!
The way I worked out the central cross is by a kind of set like approach. The cells on the line are R5-R5C5+C5 - R5C5 = R5+C5 - 2*R5C5 = 90 - 2*R5C5. But we know this is 5 lots of whatever the segments add up to. The only way this works is if R5C5 is divisible by 5 and so must be 5. Leaving the segments to then be 16.
This is the way.
Your break-in was great, helped me a lot! 😀
Loved this puzzle and the solve.
That was a remarkable setting. I had no real problem with the initial break-in but then baulked at what to do next. Once I realised that 1 was already then taken in box 4, it was clear that the 178 had to go in box 6, and suddenly the whole thing flowed out without any problems.
the nice way to do math on central box, is to see that row sum euqals to yellow+2* yellow+2* yellow=5*yellow, thus 45-central digit should be divisible by 5.
Exactly, the central line has 5 segments, so the total is 5*x. With the central cell double counted they cover the whole of row5 and col5 which add to 90.
6:50 I finished the puzzle in about two hours. I went off to pen and paper to calculate what the sum had to be of the principle three-cell segments and the four-cell diamond. The central cell had to be a multiple of five, leading to my first digit.
Region sum lines are like weird killer cages. One of my favorite sudoku variants.
Very nice puzzle. I feel like the breakin might be a bit hard for beginners because it uses geometry but after that I'd encourage new solvers to give this a go. Very instructive and fun deductions throughout the whole puzzle.
31:40 for me
nice puzzle and solving
With ur help in start.. was able to do in 18 mins..
That was a nice puzzle. I wish I would have tried it when my brain was functioning better.
Loved this puzzle so much!
Tough break in. I also liked the end and the way it collapsed.
in my case...
My break in was a bit more brutal
The Column 5+ row 5 = 90
x= value of the region sum in each region
c=central cell value
a,b,d,e = values of the central rhombus
a+b+d+e=x
2x+a+d+c+2x+b+d+c=90 = 4x + a+b+d+e +2c = 5x+2c
x=(90-2c)/5
where c is between 1 and 9
The only value where x is integer is c=5 and x=16
then the fan blades sum to 32, there are only 2 combinations of 6 numbers that sum to 32 without using the 5, those 2 combinations grouping them in 2 blocks of sum 16 are
178 349 which leaves a 26 in the middle
268 349 which leaves a 17 in the middle
The black kropki removes the 17 from the horizontal center part leaving a 26 in R5C4 and R5C6 and leave a 34 in both R6C4 and R4C6
And we can't put 178 on the left blade because that would force a 234 in R4C123 and that would conflict with the 34 in R4C6
And then 178 on the right blade forces 8 to be in R4C4 forcing 9 in R789C4 and that removes 349 from the bottom blade
From there almost everything is smooth sail
Too tough for me.
Interesting puzzle tho.
Settled for a watch.
very nice.