470 Great Ideas for a Puzzle ... ?

[00:00:14]Hello. Welcome back to Cracking the Cryptic. Now, today Simon has released his self of Rat Run 40 and it's a long video. With that in mind and conscious that Some people are very committed to watching both Cracky the Cryptic videos every day and we cannot impose ourselves on your time all the time so much. I've tried to find a puzzle that I might do in a slightly quicker time certainly than Simon's rat run puzzle but even than my average. And I remembered that we haven't been back to Richard Stokes SVS, Sudoku variant series that he publishes on Logic Masters Germany for quite a while. So I had a look at what the puzzle for this week was. What Richard does and he's a brilliant creator who's been invariant Sudoku from the absolute outset.

[00:01:12]He is in week 470, I'm not kidding you, of publishing a different rule, a diff Sudoku with a different rule set every week. And that is very impressive. He was seeing how far he could go before he ran out of ideas. Clearly not running out of ideas yet. The great thing about Richard's puzzles, he's featured in some of our apps, is that they're always enjoyable. They're never Well, never is the wrong word. They're rarely extremely difficult, but there's always a crunchy challenge and they're always fun. And that is what I'm going to have a go at today. Call it my response to the rat run if you like. Uh, but thank you Richard Stok for continuing to publish them. Um, and I will have a look at that in a moment. Uh, yes, as I say, Richard has contributed to some of our apps and do check out our apps. They are great fun. They include classic Sedoku 2 puzzles by Nikolai in that um which are superb and also um the worms and they feature a worm by well obviously by um Zeta is the latest one. It's good fun.

[00:02:27]Uh so do occupy yourselves with the apps and there's Patreon where the month Sudoku hunt is alien invasion. you can protect the future of the planet Earth, I guess, by solving solving the puzzles from other planets and uh give those a try. They're just join our Patreon. It's there's a link under the video and uh you will be able to access that. It's a competition till the 20th. There are also videos on gridoggram, new one today, on connections and on cryptic crosswords. And of course on the main channel, we do a cryptic crossword masterass on Fridays. We stream from the blueprints house, although maybe that might come to an end one day. Now, uh the last stream's worth catching up on in the in the live button, the latest VOD, our episode 48, I think. Um it was good fun. That was on Tuesday, but we'll be back there next Monday, I believe. Um and of course there's merchandise, and every day we do two Sedoku videos, Minute Cryptic and Wordle in a Minute.

[00:03:32]Check out Marty's Ratrun merch.

[00:03:35]Certainly worth commemorating. Simon Sol today. Anyway, let me have a look at the rules to harmonious thermos SVS number 470.

[00:03:45]What a number. He's going to get to 500 just after the end of this year, I think. So, anyway, let's have a look at the rules. Normal Sedoka rules apply. 1 to nine going in every row, column, and 3x3 box. Digits along a thermometer must increase from the bulb end. And the sum of the digits along a thermometer must be divisible by the number of cells the thermometer uses. This is a five cell thermometer. So its total will be divisible by five. Very simple rule set.

[00:04:17]Lovely idea. I think Richard credited Suyu, friend of the channel with the idea for this one. I'm going to start now. Let's get cracking.

[00:04:28]So yeah, box one is fully occupied by the thermos. We obviously know the total of the digits in box one because it's a secret that we sometimes share with you.

[00:04:41]It's the sum of the digits from 1 to 9.

[00:04:43]It's 45.

[00:04:46]Now if this thermo is divisible by five that takes a number divisible by five away from 45 which is divisible by five and it must leave a number that is divisible by five but that number must also be divisible by four because this thermo is four cells long and it has all the rest.

[00:05:08]So that must add up to 20. I think I'm going to write that in that form. and this one is 25. I'm going to write that in that form. Now, there are a number of ways of getting four cells to add up to 20 and then the other five will always add up to 25. So, I don't really want to try pencil marking those cuz I think I'd end up in a bit of a pickle. Let's count this one. 1 2 3 4 5 6 7 eight cells.

[00:05:41]So the total on this is divisible by eight, right? You might be thinking, well, it only uses seven cells from box 9. So that total ignores two of the numbers from 1 to nine and adds one in. But the point is all the numbers are on the same thermos, so they all have to be different. So it's using eight of the digits from 1 to 9, but it's divisible by eight.

[00:06:14]And I think therefore we can subtract from 45 until we get to a number divisible by 8 and that will be the total of this thermo and that will tell us which digit is missing from it and then we can fill the rest in unless there is very slim chance there are two numbers divisible by 8 by subtracting one sedoka digit from 45.

[00:06:36]Now the number before 45 that is divisible by 8 is 40 and that is five short of 45. So that will be the total of this thermo. 45 minus 40 tells us the number missing from this thermo and that is five. And now we can just fill in the other digits. 1 2 3 4 6 7 8 9 adding up to 40. The six in this box must go there. The five in the box must go there. And we've suddenly finished the central box.

[00:07:10]Now, that was I should have started with that thermo rather than this box I see now. But I didn't know this one. It's just going to be so much less helpful that this is seven cells long.

[00:07:26]So, it's a total divisible by seven, but it's a total that can be made up by 45 minus two different digits.

[00:07:35]And that's anywhere between 42 and 28. What totals divisible by 7 are there between 28 and 42? Well, there's 28 and 42 themselves and 35.

[00:07:51]So the total of this thermo is either 28, 35 or 42. Now it would be very constrained if it was either 28 which is missing 8 9 and therefore would require one in the bulb. Not possible. It would also be very constrained if it was 42 which would be missing the digits 1 2 and would go 3 4 5 6 7. There's our the only clash is with sevens but that's also impossible. So the total on this thermo must be 35. Unfortunately that means it's missing Oh no. This is great. It's missing two digits that add up to 10. But we know it's missing the digit one because if there was a one on this thermo, it would be here. So it's missing the digit one and it must be missing the digit nine as well to get it to get the missings to add up to 10. So this must go 2 3 4 5 6 7 8 and I think that must be right and it didn't create any clashes which you know gives gives support to my theories. Now the remaining digits in this box are 1789. This pair sees 79. So that's a 1 eight pair. This pair is a 79 pair.

[00:09:10]This thermo has a six on and either 9 or seven. And it's divisible by four.

[00:09:17]I don't Oh, that eight sorts out the 18.

[00:09:20]I don't think that's all that helpful.

[00:09:24]This digit I suppose is less than six.

[00:09:27]It can't be three or four. It can't be five because you'd have to put five and a half in here if you see what I mean.

[00:09:33]So that's one or two. Now maybe the divisibility by four is going to I don't think it's going to do a lot for me by Sudoku. This sees 8179. It has to be less than six. It has to be more than one. It's 2 three four or five.

[00:09:53]The absolute minimum total for this thermo 1 3 9 16 divisible by 4. The maximum 2 5 6 and 9. That's 22.

[00:10:07]So the thermo total is either 16 or 20, but there's a bit of variability there.

[00:10:12]So let's pencil mark these digits. We've got 4 7 8 9 still to place in this column. This one can't be nine.

[00:10:22]And this one therefore can't be the lowest of those digits. So it can't be four.

[00:10:30]Oh, if that's a four, this one can't be 2, three, or four and would have to be one. So this thermo then would be 1 + 4 + 7 to make it divisible by three. I'm using the old trick of any number divisible by three has its digits divisible by three.

[00:10:54]It's digit sum. That's what I mean. Oh, I don't know. Okay. So, it might begin.

[00:11:00]That might be a four. If that was an eight, this would be a nine. And this would be 1 14 or 7.

[00:11:10]And it could be one or seven.

[00:11:12]Oh, well, I don't know. Okay, that is a 235 triple by just elimination here.

[00:11:20]How about marking up this thermo?

[00:11:22]Actually, this is quite interesting. The digits available are 1 3 4 8 9. We can eliminate one. If one appears on a thermo, it must be on the bulb. We can eliminate nine because if nine appears on a thermo, it must be on the tip. I think we can eliminate eight because if eight appeared on this thermo in one of those positions, that would be nine and it can't be. Therefore, this is a three four pair and we know the order from the from the direction of the thermo. This digit is 1 or two. This one is now 5 6 or 7. And this thermo has to add up to a total divisible by four. We've got a minimum of 1 345 which is 13. We've got a maximum of 2 3 47 which is 16.

[00:12:12]13, 14, 15 or 16. The only one divisible by four is 16.

[00:12:20]And that's what the total must be. And that was the maximum. So this is maximized. That is maximized. And that thermo is done. That two has forced this to be a one. We can take three out of this cell as a possibility. We've got 189 to fit in row five.

[00:12:40]This digit I'm going to just do that. It can't be 1 2 3 4 7 8 or nine. That's five or six. All we know about this thermo is it's got an even total. It's divisible by two. So if that's odd, that's odd. And if that's even, that's even.

[00:12:59]Does limit this a bit. Um, now what about this one then? So we've now got a definite one and a definite six. They add up to seven. Minima gets us to 16. Maxima gets us to 21. So it's 16 or 20. I might have known that before.

[00:13:28]Oh, that's quite interesting. To get to the So the minimum would go 1267.

[00:13:37]The maximum we'd have to take one off the possible maxima here to get to 20 and you couldn't take it off there because you can only take two off. So it would be here. So this would go 1469.

[00:13:50]So this can't be a five anymore. That is two or four.

[00:13:55]I may be complicating this wildly now.

[00:13:59]Oh yes, look 2 three four in this row.

[00:14:02]That is a triple here. So that digit is five or six.

[00:14:07]These are from 189.

[00:14:12]I'm wondering if this little bit of information can be transferred up here and help, but I'm not sure. I think I need more information to to approach these 20 and 25 totals that I worked out in box one.

[00:14:31]Um, don't know about that. Right. Maybe I need to focus on this little three seller.

[00:14:38]Yeah, I do. Two, three, or five there.

[00:14:40]And this can't be eight or four. This is 1, six, or 7.

[00:14:46]Now, this thermo could go 7 8 9 and it would definitely be divisible by three. Then it would add up to 24.

[00:14:59]But it could go 6 78. And there are various possibilities I think that begin with a one. So I don't think that's actually as helpful as I was wanting at the moment.

[00:15:11]Oh, okay. Six can't go in these cells.

[00:15:14]Nor can seven.

[00:15:18]But let's think about six.

[00:15:24]If six went in one of these two cells, these would have to be selected from 7 8 9. But that just wouldn't work with that seven there.

[00:15:36]So six doesn't go on this thermo at all.

[00:15:39]Six must go on this thermo.

[00:15:43]And the position it's in, well, I don't know.

[00:15:47]I'm going to remove these total markings. Now, six is on this thermo.

[00:15:51]This thermo adds up to 20.

[00:15:54]Yeah, that's interesting. The total adds up to 20. So, six can't be at the end because the maximum total you could get to is 18. 6543.

[00:16:06]Six. If it was here, then the minimum would be 678 for those three cells, which is 21. So, the six must be here. This digit is seven or nine. If it's seven, these two add up to five.

[00:16:23]and are either 52 or 3 4.

[00:16:28]If it's a nine, these two add up to five. Oh, no, sorry. If it's a seven, 13, those two add up to seven and either 52 or 3 4. If it's a nine, that's when they add up to five and they're either 1 2 sorry 1 4 or 2 3. So, we did get quite constrained. Now, seven also can't go on this thermo because it can't go in those cells.

[00:16:55]And if it went in one of these, these would have to these would be impossible.

[00:16:59]There aren't enough high digits. So, seven does go there. And now these two do add up to five.

[00:17:06]And now we know where 9 and 8 go in the box by thermo rules. 98.

[00:17:14]And that's the other digit from one and two. That's the other digit from three and four and that's a five. Now there's a one two pair looking at that cell and that one. Now there's a three four pair.

[00:17:26]Now we have to fit 8, seven into this column. It's a lovely puzzle, isn't it?

[00:17:30]8 and seven go there. These ones are five, six, and nine. That one in the corner must be a nine. It's a naked single.

[00:17:38]This digit is also a naked single. It sees 9 5 6 8 7 in the box. 431 in the row. That's a two and that places two here in box four.

[00:17:50]That is a naked one. Nine and five go in there. This digit has become a one.

[00:17:58]And in this column we've got a three four pair. This digits a one.

[00:18:05]Now yeah those are going to add up to five. So there so are those. We can take five out of that cell. We can take six out of here and eight out of here and seven out of here. And this has got all very restricted. It could still be 789.

[00:18:22]Actually, it could be 189 or 147 as well.

[00:18:27]Not 100% sure. There aren't other possibilities, too. So, I'll have to slow down on that. These digits are from 569. These ones are from 3 478.

[00:18:40]That one can't be four. This can't be three or seven.

[00:18:45]I'd quite like to spot some sort of double or triple at this point. Oh, hang on. These are from 1679 in the column. So, that's a group of 1679. And that digit is part of a 48 pair. Now, that's not as helpful as I wanted it to be.

[00:19:06]I've still got this. Oh, no. I've got this one to resolve. Now, what were the two possibilities here? One of them was 2 and 7 to make the thermo add up to 16.

[00:19:20]That seems to still work. The other one was 4 and 9 to make it add up to 20.

[00:19:27]479138.

[00:19:30]That would have to be five or six. And this digit would be two.

[00:19:35]Does anything else bad happen with a four here?

[00:19:40]Oh, well, nine there makes that a nine.

[00:19:48]I don't know. It's not. Oh, 7 9 pair looking at this cell. So that's eight.

[00:19:53]And now this must be even as well to make the thermo add up to an even number and be divisible by two. That eight has seen this 98 pair as well. So box six is finished. This digits a four. Four. That sorts out three and four. These are now a seven eight pair and we know the order. That can't be nine or five.

[00:20:16]Everything is falling into place. That's a nine. This can't be four. So that's two. And now this must be seven. And this thermo adds up to 16.

[00:20:26]And well, all the thermos apart from that three cell one are sorted out as long as we make these pairs add up to five. Okay, that's a two four pair. This is a 379 triple. And we know that one's a three. And there's a 79 pair. And look at this. 7 9 are a pair in the row. And that becomes one.

[00:20:48]I thought that was going to do more.

[00:20:49]That takes one out of these cells. And this one has 79 in the row as well.

[00:20:54]That's a six. Now, I still can't resolve this. 793248 165. I can fill those in. 51 6. That one sees this bulb. That's a two. This must be a three. And now this thermo adds up to It doesn't seem to add up to 20.

[00:21:20]I've got my numbering wrong up here.

[00:21:24]Oh, botheration.

[00:21:29]Right. I mismarked that box. I know where to come back and get things fixed in a moment, but I mismarked this box number one. That's so long ago. I'm such a numpty. And well done if you pointed it out in the comments. You were right.

[00:21:45]So, I got to this point and I already mismarked it. These two had to be left adding up to seven, not to five. That was my miscalculation.

[00:21:58]So, that's two or three. This one is four or five. Now we can still fill in nine and eight in the box.

[00:22:07]And we've got two digits from one, two, three, and then one from four or five, which is different from my earlier pencil marking. Seven and nine are still looking across here to make that eight.

[00:22:19]By par, that's a six. That's a five. Now we get eight here.

[00:22:25]Uh we can actually even place eight now in row five there.

[00:22:33]Yeah, I mean this still ought to go swimmingly. He said with a with un undue confidence.

[00:22:41]What am I trying to do here? 1579. But seven can't be in any of these cells. So seven is there in the box.

[00:22:50]That can't be nine.

[00:22:54]Now what else? I worked on this, didn't I? How did we get that? We had these being from 1679. That's true. This can't be eight. So, we've got the quad.

[00:23:06]This digit has to be four, I think. Now, haven't seen that before, but I think it's right. This one is eight in the box.

[00:23:19]Okay, that's good. That's good. Good.

[00:23:21]Good. Uh, there was some two, three. Oh, no. I had a quad here, didn't I? But I don't have that anymore.

[00:23:30]Well, you know, that's what happens when you make a mistake and you have to unwind it sometimes.

[00:23:36]Um, right. So, it's a slightly different puzzle. Now, that can't be seven or nine in the row.

[00:23:44]That can't be six. Now, here if that can't be seven by thermo rules. So, we've got one and four and we need a seven to make that divisible by three.

[00:23:56]Well, that makes me happier because it means we've resolved lots of cells in this box.

[00:24:05]Right now, this row, we need a one. We can place that. This is three or five.

[00:24:11]Uh, why can't we sort out that one?

[00:24:14]Because we haven't resolved this 159 triple.

[00:24:21]Yeah. Yeah. It's a little less uncert.

[00:24:24]It's a little less certain than it was before. Now, how about two in this box?

[00:24:28]Not in those cells. How did I get it here? I don't know. I don't think it worked. Ah, eight. I found in box nine.

[00:24:39]That can't be seven or nine.

[00:24:42]So, it's three or five. Making a pair with that. Then we can fit in seven and nine in the column. I keep hoping that's going to ramify over here, but it doesn't do it. Three is in one of those cells.

[00:24:54]No, that's not necessarily true.

[00:24:58]8 519. We need a seven here in the corner.

[00:25:04]There's a nine in one of those. So nine has to be in one of these two cells.

[00:25:10]Uh that's not utterly useful.

[00:25:18]Oh, this pair. No, they're not resolved yet. And that must leave this unresolved as well.

[00:25:25]So it's going to be this thermo next that unsticks us somehow. So let's work through the possibilities again. If that's a four, that's Oh, look. We've got a nine at the top of the grid. So we don't need to work through the possibilities. We just need to solve that. Add up the thermo. 13 14. That's a two. That's now six.

[00:25:47]Um, in this row perhaps? No. In this box perhaps?

[00:25:56]In this column perhaps? We've got two, three, and four still to fit in.

[00:26:02]Now, that feels like a quad. Yes, it doesn't have six in. So, six is placed in the row.

[00:26:09]This is not allowed to be two or three.

[00:26:11]So, four or five there. And that's a pair in the row.

[00:26:17]It's so pretty actually. Um, now I still don't know where nine goes there. We need a six in this row. I found it.

[00:26:29]6 8 7.

[00:26:32]So this is either a three four pair which would make that 2 one five on top of nine at the bottom or this is a two five pair. one that would be nine and we'd have a three four pair. Those are different. There's no overlap. This digit then is three, four or five in the row. That's five or nine.

[00:26:58]These are from 259. Full pencil mark mode. Now it's just box one where the thermos are left, isn't it? 6528713.

[00:27:09]That's four or nine. This is a sort of chocolate teapot quad. Uh, one and three have to fit into these cells along with one of four or nine.

[00:27:24]I'm going to have to work it out through here. Right. If that was a five, this would be a five. That would be a five.

[00:27:35]That would be a five. That would be a five.

[00:27:40]Alternatively, this is a five and then that's a five anyway. So that cell is always a five. That's a one. That's a nine. One and nine there.

[00:27:52]Um that 59 sees this cell and makes it a two.

[00:28:00]That stops this being a two and this one. This is one, three or four.

[00:28:08]One of those is a two.

[00:28:13]Now soon this pair is going to suddenly reveal itself but not yet. 98617.

[00:28:22]This is three or four in this column.

[00:28:27]And and where does that put it? 65287 in the row 1 3 4 or nine here. Oh goodness. Still not done.

[00:28:39]So, I'm going to have to think yet again about right if that's a three four pair.

[00:28:44]Oh, where's the one in the bulb? One can't be on there. It's not a bulb. It's really very straightforward when you get this far and I just can't see it. Right, this thermo now does add up to 20. This one now does add up to 25. And those were the key targets. So this has become a four. This is not a two. That four sorts out the quad down here. 9 five 3 4. This is five. This is nine.

[00:29:20]That's three or four. This is one.

[00:29:23]This is four. That's three and two.

[00:29:27]That's three and four.

[00:29:30]This one is five.

[00:29:33]Two and three.

[00:29:36]two, five, and three. And that is the solution. I don't think this had the solution input. So, I will make sure that when you're solving it, it does have it. But those thermos are now harmonious. Thank you, Richard. I managed to take 10 minutes longer by making an arithmetical error up here than I needed to, but it was exactly the sort of puzzle I wanted to be doing. So, well done for creating it. And thank you guys for following us at all.

[00:30:03]Leave me a message if you've got time, but uh only if you happen to see this after you've watched Rat Run, presumably. Bye for now. Thanks for watching.