Help with riddle

My calendar gave me the following riddle on January 4th:

The solution it gave yesterday is:
image

I understand the text (you can add 「をつく」 to all the words in the category 「ある」), but I do not understand how the words in the category 「なし」 are related to this. Is this a common kind of riddles in Japan? Can somebody explain its principles?

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The なし ones are basically there to test hypotheses against. If you think of something that works with the ある column, but it also works with the なし column, then you’d be able to rule it out as a solution.

They’re also thematically paired, the same way 鼻 and 耳 are. The なし column isn’t just random words that don’t take をつく, they have some other relation to the words that do.

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Thanks.
Do you think that this riddle could be easily solved by native speakers? No way for me as I didn’t know most of those expressions (to be honest I only have encountered 嘘を吐く).

I just asked my Japanese wife and she wasn’t able to solve it. (She only tried for a minute or so before looking at the answer). So it seems to be relatively tricky even for native speakers.

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My wife got it, but only after I told her it was を(something) that attaches. She’s not a big puzzle person though.

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If they read the hint at the bottom, I think they’d get it easy.

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Apparently not.

I got the idea thanks to the hint, because it had the word つきます, which immediately made me think of 嘘をつく and 餅をつく. I didn’t know any of the other 3 expressions, so I couldn’t get the answer though :sweat_smile: I don’t know if they did it on purpose, but it’s a very big hint.

(Then I realized the answer was in the next image, haha)

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