Lady Or The Tiger: The Classic Riddle

*** Today's Sudoku***

We love innovations in sudoku and ZegreS' idea to make sudokus that are hybrids with famous riddles tickles us pink. We did one of these a couple of weeks ago and here's another one! This time it borrows from a famous riddle in The Lady Or The Tiger by Raymond Smullyan. Who would be the reward behind the door if you had a choice? If we get enough replies we'll reveal our most desired party guests X)

You can play it at the link below:

https://app.crackingthecryptic.com/sudoku/6nb6Ndf63L

Rules:
Riddle part:
A lovably eccentric king has put before you a test. Choose one of three doors and encounter either: a lady (represented by the digit 1) who is the life and soul of a party or a tiger (represented by the digit 9) struggling with intermittent fasting. Behind two doors (in the cage) is a tiger (9) and no lady (1). Behind one door (in the cage) is a lady (1) and no tiger (9). Signs hang above each door: Above Room 1: A tiger is in room 2. Above Room 2: A tiger is in this room. Above Room 3: A tiger is in room 1. The king tells you: The sign on the room with the lady is TRUE and at least one of the other signs is FALSE. Answer the riddle, solve the sudoku, don't get eaten.

Sudoku part (having noted the implications for the digits 1 and 9 from the riddle part above):
Normal sudoku rules apply. In cages, digits sum to the small clue in the top left corner of the cage. Digits along an arrow sum to the digit in that arrow’s circle. Cells with a grey circle must contain an odd digit. Cells separated by a white dot must contain consecutive digits. Cells separated by a black dot contain digits with a ratio of 1:2. Not all dots are given.

If you'd like to try jovi_al's Negativity - an amazing new classic sudoku - then you can at the following link:
https://app.crackingthecryptic.com/sudoku/mdtTb9qmhp

Rules:
Normal sudoku rules apply.

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Видео Lady Or The Tiger: The Classic Riddle канала Cracking The Cryptic