Find the Bogus Amogus

Normal sudoku rules apply. A cell with a circle contains an odd digit. A cell with a square contains an even digit. HOWEVER exactly one of the given symbols is a liar. It may be a square containing an odd digit or a circle containing an even digit.

On our new app, there's a FREE pack of puzzles by Prasanna Seshadri and a paid pack: DOMINO SUDOKU! Prasanna's free pack includes one puzzle for each variant of our existing apps. Domino Sudoku is a pack of 100 handmade puzzles (40 on launch, 5 added each month for a year) by some of the best constructors in the world.
The app is coming very soon to Steam as well - but releasing it is in their control.

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Tim McCaskey (Guitar) or Lucy Audrin (Piano) or Riffclown plays Mozart's Sonata no 16 ("Sonata Facile")
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Play the puzzle in the video by clicking the link under the video (above). Thanks to Sam Cappleman-Lynes and Sven Neumann for their work.
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Joel Blundell

▶ABOUT US◀
Hi! We're Simon Anthony and Mark Goodliffe, two of the UK's most enthusiastic puzzle solvers. We have both represented the UK at the World Sudoku Championships and the World Puzzle Championships. We're also "cryptic crossword" aficionados. Mark is the twelve-time winner of The Times championship and Simon is the former record holder for most consecutive correct solutions to The Listener crossword. We hope we can help your puzzle solving while also introducing you to some of the world's best puzzles.

Thank you for watching!
Simon and Mark

[StNeurion]

The use of the Liar Clue was sublime by the setter. It caused enough doubt to slow the solver from just filling in the grid, but gave so much meaningful information to be used at any given time. Until the crux when the Liar Clue is finally singled out! A big thank you and congratulations to Bastien for coming up with this one.

[RADZIO]

24:35 for me. At first I was afraid of it, since "Any of these could be any number until I find the impostor", but the fact that there can only be 1 fake one made a bunch of interesting restrictions

[pbush]

My favorite part of this puzzle was that my gut instinct was that I'd find the liar cell and then the puzzle would fall apart, but it was literally the last available clue.

[shiruGT]

the second puzzle from this channel i solved by myself without needing help. took me about an hour, but hey - baby steps!

[MostlyHarmlessPlanet]

36:34 Took me a while to understand how the "only one liar" fact can be used to rule out numbers which would cause two liars in a box, especially 7 in box 4, evens in box 6, and 6's in box 8.

[torstenaan]

Brilliant puzzle. Finding the cells that couldn't be the liar resulted in the last one being the liar. Well set!

[heatherfyffe]

I think there's a simpler way to think about the 'cracking in' logic that he resolves by painstakingly figuring 'if this one is a 4 then it's a liar and that would force this other one to be a liar...'. It's the same basic logic, but applied in general terms to the whole box at once. For boxes 2, 4, 6, 8, all cells but 1 are given a shape OR a given digit, which obviously assigns the even/odd parity for those cells. For instance, box 2 starts by saying there are 4 odd and 4 even and one unknown. If they're all telling the truth then the blank cell is odd. But if one of them is lying, it MUST be one of the even cells - if one of the odd cells were lying, it would be even, and then there would be too many even cells. Therefore, all of the ODD cells are confirmed truth-tellers. This logic applies to all 4 of those boxes (some going the other way around).

I can't claim that I realized this easily heh. I dabbled around in this puzzle using all kinds of strategies including dumb luck guessing, to see what would happen and to help me understand how the puzzle restrictions worked with each other. Of course I ended up with that same deadly pair set as so many others did.

But finally I figured out that I had to start by ignoring the shapes completely and just doing as much as I could through pure sudoku. Then I coloured every confirmed digit (colouring all of them helps me see the patterns more easily) and was able to confirm a few shapes as being definite truth-tellers (eg because there were 4 confirmed even digits then the remaining unknown cells had to be odd), and was able to progress along this way, pure sudoku and colouring as I went, until I reached those last 3 possible liar cells and it was impossible to go any further. Exactly as he did, there it could be seen that if that one was 2 then that other one would also be 2 and therefore it had to be the 3rd as the liar.

The whole thing took me 10 minutes... once I'd figured out how to do it. Which I won't tell you how long that took hahaaaa

[DNPaterson]

30:14! This was a nice approachable puzzle, and I didn't even have to check the video for clues 😃

[mipsuperk]

Seeing things get uncolored is so refreshing.

[alexholker]

I usually skip these "one of these rules is a lie" puzzles, but I liked this one. There was enough reliable information that I was able to start figuring out where the ambiguous rule could not be false, rather than quitting once I found a snarl of unreliable possibilities.

[ericpraline]

What an exceedingly clever puzzle. I feel I had to make a lot of deductions to crack it. The coup de grace is the unmasking of the liar right at the end.

[Anne_Mahoney]

I'm thinking it's time to get me a copy of Bastien's book, maybe as a back-to-school treat. If I finish writing all those first-week handouts I can reward myself!

[christianarbeiter]

Thanks for the work you are doing. I enjoy it every day!

[andyparkerson]

31:40. Great solve path. I usually stay away from liar puzzles, but this one was excellent!

[MonkehBuns]

"Imagine if it's just sudoku and I've been panicking" should be the channel slogan.

[steve]

27:04 for me. Got a good laugh out of that liar - that was definitely worth (more than) the price of admission.

[victorfinberg]

On my first try, I just wandered around for a while, and was unable to finish. On my second try, I assumed that all the clues were correct, and got to the end, except there was a deadly pattern on 4x46 pairs. Third try's a charm. The trick is to recognize the logic Mark explains at 9:25 early.

17:30 Mark: "I'm going to complete the pencil marking now." ACHIEVEMENT UNLOCKED

Now space the imposter

[TurquoizeGoldscraper]

34:16 for me - The rule made me doubt every odd-even and all it did was to disambiguate the last number when I verified the others were all correct.

[andyhoudini]

I used colours to show definitely odd and definitely even cells and used rows and columns too (5 odd/4 even).
Got to a point when only one greyed cell was left uncoloured, which had to be the liar.

[davidh.]

44:20. Not being particularly clever, I simply pencil-marked the whole grid first, then started eliminating the ones that could not be lying. It was slow, but effective.