Logic Masters Deutschland e.V.

Pythagoras Triangles

(Published on 1. March 2023, 05:00 by Will Power)

Normal Sudoku rules apply. Numbers on triangles represent a unique right triangle for each color. The size of the triangle is found by ADDING the two numbers on each side to get a 3-4-5 triangle, a 6-8-10 triangle or a 9-12-15 triangle. The largest sum added will always be the diagonal of the triangle. (The example triangle has 4, 5 and 6 at the corners. This would represent a 9-10-11 triangle, which is not a Pythagoras Triangle.) ONE OF THE COLORS IS A LIAR. The numbers on this color do not make a 3-4-5, a 6-8-10 or 9-12-15 triangle, and might not have the largest sum on the diagonal. ALL FOUR COLORS each have the same three numbers and sums on them. All possible triangles are shown. Numbers in cages sum to the number in the top left corner of the cage. Numbers with a white dot between them are consecutive. Not all possible dots are shown. Note for colorblind people: There are 8 Red, 5 Purple, 5 Blue, and 4 Yellow triangles shown.

F-Puzzles

Solve on CTC

Solution code: Row 3 and column 3.

Last changed on on 27. March 2023, 18:02
Solved by TeamSchmidt, metacom, zrbakhtiar, Chelo, kublai, Mr.CHEN, Myreque, scushuaishuai, sirtramola, MarthaB, mcc, AvonD, -Tsigje-, Geryyy, pjhiatt, geronimo92, heatdevil, peep50183, Dermerlin, Taratang, josemadre, tobymgk, dlandrum17, FlashZange, Montikulum, Krokant, Saskia, drf93, martin1456, extremelypuzzled, Kekes, Tiffanatisk
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Comments

on 27. March 2023, 17:58 by Will Power
Revised rules for clarity of the liar triangles.

on 21. March 2023, 05:19 by dlandrum17
I went and found this puzzle because you had mentioned it @Will Power. I like the premise and the colors but I feel like I there wasn't a definitive break-in or aha moment. I observed about the overlapping digits in the trios and kind of tested one way out and it happened to work. It just felt like I stumbled through it all by happenstance than a more definite proof.

Last changed on 12. March 2023, 07:25

on 12. March 2023, 07:24 by Will Power
@peep50183 Once you know the 3 numbers in EACH of the three correct triangle types, the overlapping becomes apparent on the grid. The three correct triangles overlap in a way that the LIAR cannot. Thanks for playing and commenting. -Will Power

on 3. March 2023, 00:08 by peep50183
Although I spent ages (probably too long, ha) trying to prove which of the triangles had to be the liar, I had fun with this - thank you :)

Last changed on 1. March 2023, 18:58

on 1. March 2023, 18:56 by Will Power
Added text including "SUM" to differentiate the side length of the triangles from the actual "NUMBERS" in the grid. Thanks to @crhodgkin for commenting.

on 1. March 2023, 17:22 by MarthaB
Thoroughly enjoyed this puzzle. Once the triangles are determined, it falls out easily.

Last changed on 1. March 2023, 18:53

on 1. March 2023, 14:07 by Mr.CHEN
A fake triangle does not need to satisfy the same relative position of three numbers, but only needs to satisfy the same group of numbers? I found that it seems impossible to satisfy the same position at the same time.

@Mr.CHEN Thank you for your question. I tried to be clear that all rules BEFORE the LIAR statement do not need to be followed by the LIAR. Statements after the LIAR statement are followed by all. Happy puzzling, -Will Power

Difficulty:2
Rating:76 %
Solved:32 times
Observed:3 times
ID:000D30
Variant combination
Sudoku, Consecutive Pairs (Variant), Killer (Variant)

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Solution code:

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