Pumpkin Pi

Logic Level 5

You baked a nice delicious looking pumpkin \(\pi\), cut it into 6 slices and served it on your table, as a fan of numbers, you labelled each slice with numbers from 1 to 6.

While still feeling very pleased and satisfied, you went back into your kitchen to grab a glass of water, but once you got back to your table, instead of finding your pumpkin \(\pi\), you found yourself a piece of paper with a pumpkin \(\pi\) drawn on it with the labelled numbers replaced by alphabets (as shown above).

Oh no, that's not good news.

You looked at the back of the paper and found a message that reads:

"Harhar... want to get your pumkpin \(\pi\) back??? Not until you tell me the numbers labelled on your \(\pi\)."

Bummer, having a terrible memory, you have absolutely no idea how you labelled your \(\pi\).

You continued reading the message:

"Don't worry! Just in case you forget, I had left a liiiiiiitle bit of clue on 6 seperate pieces of paper, but mind you... I'm not always honest..."

Surprisingly, you found 6 pieces of paper under your table, each one reads:

"1---- is adjacent to 4; is adjacent to 3"

"2---- is adjacent to 4; is at the opposite of 6"

"3---- is at the opposite of 4; is adjacent to 5"

"4---- is adjacent to 6; is not adjacent to 5"

"5---- is adjacent to 3; is not adjacent to 6"

"6---- is not at the opposite of 3; is not adjacent to 1"

Each piece of paper contains 2 information about how your numbers are labelled, and also you know that on every paper, one of the information is true while the other is false.

Can you deduce the numbers labelled on your pumpkin \(\pi\)?

Give your answer by concatenating A, B, C, D, E and F, assuming A is 1, forming a 6-digit number, for example, if you think A, B, C, D, E, F are 1, 6, 5, 4, 3, 2 respectively, then your answer should be 165432. If you have multiple answers, give out the smallest one.

(Note: If 2 slices are next to each other, then they are adjacent e.g. A and B, if 2 slices have other 2 slices between them, then they are opposite to each other e.g. A and D)


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