Sudoku Adventure - "Multiplication sign" by PjoeterBliep

[00:00:00]Hello, let's continue our Sudoku adventure with multiplication sign by pewter bleep. So we have normal 6 by 6 Sudoku rules. That means in each row, each column, and each 2 by 3 box, we are placing the digits 1 to 6 exactly once each. We also have these numbers outside the grid.

[00:00:15]They are the product of the first n digits in its row or column where n is the closest digit. So if this was a three, that would mean these three multiply to 360.

[00:00:26]And if this was four, then these four would multiply to 360. And that's it.

[00:00:30]Those are the rules. There's a link in the description if you'd like to try the puzzle yourself. And I'm going to get started right now.

[00:00:37]All right. I'm going to start with the small digits here. Uh small product. So the smallest product is 15.

[00:00:43]I think prime factorizations are helpful here. 15 is 3 * 5. I'm just writing that out as a note.

[00:00:48]And so we're going to use the three, we're going to use the five, but we have to That That means we can't use the two.

[00:00:54]So it's not going to be two digits three five. It's going to be three digits.

[00:00:59]And so we're going to have to use the one.

[00:01:01]Just to pad that out. So this is 1 3 5.

[00:01:04]And so this is 2 4 6. That makes this 2 4 6 and this is 1 3 5.

[00:01:08]All right. Well, we're not doing 60 and one.

[00:01:12]I don't think we can do Can we do 60 and five?

[00:01:16]All right. So the way to think about five is what's the digit that's outside.

[00:01:19]So 6! is 720.

[00:01:24]I I did some studying before this.

[00:01:26]>> [laughter] >> Um 6! is 720. So the outie of our 60 is going to be um some number of digits that have a product of 720 divided by 60. So that's going to be 72 divided by 6. That's going to be 12.

[00:01:46]Um pretty sure I did that right.

[00:01:48]Yep. So whatever the outies are multiply to 12.

[00:01:52]So if this was a five, I'd have to put a 12 here. That's not going to work. So this is a three.

[00:01:57]Um So, the Audi's multiply These three multiply to 12.

[00:02:02]The So, this is three already. These two multiply to 20.

[00:02:06]So, they have to be four, five.

[00:02:09]That's four, that's five. Okay, that's not a four.

[00:02:12]Um and so then this is going to be one, two, six, which does multiply to 12.

[00:02:18]All right, I'm going to think about the 360 now cuz we can do the Audi trick.

[00:02:21]Sev- 720 / 360 is two.

[00:02:24]So, we're either going to have a a single Well, we can't have a singular two out here because this can't be five.

[00:02:28]So, this is going to be a one, two pair as our Audi's, which still multiply to two.

[00:02:32]That's going to be our five, and that's going to be a four.

[00:02:36]All right, so that's one.

[00:02:39]And then this is a three, six pair.

[00:02:44]So, we have the 24 and we have the 60. I want to think about this 60.

[00:02:48]So, we know this isn't going to be three, four, five, but if we think about the Let's think about the prime factorization of 60. It is two, two, which brings us to 20.

[00:03:01]No, not 20.

[00:03:03]15. So, it's two, two, three, five.

[00:03:06]Right, which is why three, four, five works, of course.

[00:03:09]Could have just looked at this. Two, two, three, five. Uh so, I think we're going to have to include a one here.

[00:03:15]We have two, two, three, five. I'm just Let me just do it here. Two, two, three, five. These are our prime factors. We're going to have to We're going to have to get We can't repeat the two. So, but the very So, we're going to have to either We're going to have to combine the two into one of these.

[00:03:28]Um If we combine the two and the two, we get three, four, five. And so, we could do a Problem with three Oh, yeah, and three, four, five is nice because that's going to be a four.

[00:03:38]This can be a four, and then we could do a one, three, five across here.

[00:03:42]Um Is there any other way to combine though? Like we could do two times three is six.

[00:03:48]Which unfortunately, we have to use one of these numbers first. It's not going to be five or six and the two doesn't work either. We can't do two times 30.

[00:03:55]So I think that's it. I think we have the the four here.

[00:03:59]And then the five has to go here and then this is one and this is three.

[00:04:03]Gives us the six and three here. These aren't one.

[00:04:06]This is a two-six pair.

[00:04:12]I'm a little worried at what's going to resolve Oh, is the 15 going to resolve this? No.

[00:04:17]The 24 is going to resolve it. Okay, good. I was like what resolves this deadly product? Um let's just do as much Sudoku as we can. That's a two. That's six and two.

[00:04:24]This is a We need the one and we need the four. Okay, so what are these pairs?

[00:04:29]This is a four-five pair. This is a three-six pair.

[00:04:32]Um All right, this is important. This is one four or five. Well, certainly not going to be a one multiplying to 24.

[00:04:40]Um five is way too big to to multiply to 24. It was too big to multiply it to 60.

[00:04:46]So this is four.

[00:04:49]So these four digits multiply to 24. It looks like it's going to be two, three, four.

[00:04:55]Okay, that's five and four. Five doesn't even go into 24. So that's a one.

[00:04:58]Um these multiply to 12. We need the two here, yeah. Six, six, two, five, one.

[00:05:03]That's two, one. That's six, two. That's three, six. This is the three and the five and we're done. All right.

[00:05:09]Dee dee doo ding.

[00:05:11]Nice, that was a cool puzzle here, bleep. Um It's interesting cuz the one really throws you like the one adds flexibility, right? Because it can be part of the product or not depending on how many digits you want to include.

[00:05:26]So that that's pretty neat property.

[00:05:28]With sums you don't get that you cuz you don't use zero. I mean there are puzzles where you can use zero.

[00:05:33]But uh in fact uh X-sum puzzles are particularly interesting when you can use zero.

[00:05:38]And so this is kind of a an analog to that.

[00:05:41]Very nice. Well, how did you do?

[00:06:02]>> Hey.