Logic Masters Deutschland e.V.

Standard sudoku rules applies. Fill the grid with numbers from 1 to 9(6) so each digit occurs exactly once in every row, column and 3x3 box.

Given digits at the left and right is the tens digit in the three digit number it’s in. In every row, the two three digit numbers sum is integral times multiple of the three digit number in the first row.

The last puzzle is an example, you don’t need to solve it. So in every row with two reds, left plus right equals integral times of top.

6x6 version, the two digit number on the left plus the one on the right is integral times of the two digit number at the top.

The first puzzle is made by Old Miles from China. He think extra width made it looks thick, so he choose to only show the tens digit. Understandable, in couplets, the horizontal scroll is wider than first and second line of the couplet. It needs to be put on and beside the door, so it has to looks like a door, not changing the shape. Me, i just keep a door shape hole in the middle to mimic the couplet. I don’t want to trouble myself with the rules explaining. The whole puzzle should click if one looks at it and see some words and guess the real rule.(why i explain this in English, do people know what a couplet is)

About this puzzle, i, hmmm. I was going to make a firework related puzzle, but i thought, nah, too hard, maybe this idea would be easier. And theory happens. Old Miles said the calculation is going to be a torture, so we have to try to make it easy. At first, he try to made left right four digit number and i said, no, i can’t deal with this level of calculation. So three is max. The max calculation should be at around 1830. now, i need things to disarm people’s fear for calculation, start with last digit. 5 is a good choice, so is other odd digit. Even digit is way too scary. Than, i need to try to max the first digit without clearing too much combination. So it’s fix to 235, 6 combination is enough torturing.

Spoilers warning. You’ve been warned. Once listing the tens digit doesn’t have that much choice. Tens digit can only plus one. And all these 6 combination has a relatively wide tens digit. Here’s a theory i know might be there but i don’t want to know. Tens digit may have a slightly large pool than the last digit in multiplication. I just don’t have the patience to list every combination, 99, no, to find out which one has a small pool. But Old Miles and I did found some other conclusion, like 7 row is hard to find. It’s so easy to no solution to this whole rule if the top digit is chosen in some way. Even in 6X6, i don’t know how to create a fifth row. It’s hard for me to find solution but maybe software can help(i don’t know, i never learn those)

Last, this is my version of the idea. Would i set another one like those? No, i’m going to stay away from mixing plus and multiple for a long long time.