You've got a few options here, as I should think that ultimately the solution will be found by the not-sphynx's behaviours and mannerisms (though the questions themselves do help bring those behaviours out).

You could go for something everyone knows, like "What's lighter: a tonne of bricks or a tonne of feathers?" When the players get it right by saying they both weigh a tonne, have the not-sphynx insist on the obvious wrong answer instead (the feathers, as a single feather is lighter than a single brick). Then when the players explain why that's wrong and their answer is right, the not-sphynx pretends he knew that and was just testing them. Stuff like that.

If the campaign isn't super serious in tone, you could work-in famous pop-culture examples. Ask the questions for crossing the bridge from Monty Python "What's your name/quest/favourite colour?" With the not-sphynx not getting that the difficulty came from Tim alternating to a super hard third question for every other person he asked. You can even use the question about the African Swallow, with the not-sphynx not knowing if it should be laden or unladen, and just handwaving that one away when the players ask.

Ask the "What have I got in my pocket" question from the Hobbit. The players might try and answer "The One Ring" or something clever. When they exhaust their ideas and give up, the not-sphynx gets embarrassed and plays it down, admitting he forgot he doesn't have any pockets...

Cool idea overall though - I think your group will have a lot of fun.