The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.


Round 3

1. Ivan, the Palindrome Man, has a clock that shows 24-hour time in the following format: HH:MM:SS Eg. 23:12:41, 03:56:07. Naturally, he gets excited when his digital clock displays a palindrome time. For how much time each day does it show a palindrome time?

2. A paragraph puzzle! Competition's had none of those yet. Bad grammar, huh? Hard to write! Can't express myself properly. Hard picking suitable words. Why? Is it just me? Identify rule to writing. Difficult problem: say why. Answering better means more points to you. Good luck, puzzlers.

3. At the inaugural Grey Labyrinth convention, there were souvenir clocks for sale. These featured a minotaur on the face, where the minotaur’s left and right arms were the hour and minute hands respectively. Cute stuff. Paladin was in put charge of the promotional display. He arranged the clocks on a shelf and deliberately set them to show specific times. None of them got wound, and they didn’t have batteries, so the times they were set on never changed during the conference. After the conference (featuring lots of great puzzling and a guest appearance from a real live kakapo), Paladin returned to pack up the display. The clocks on display showed the following times (left to right): 4:30; 2:47; 1:30; 2:52; (space); 1:38; (space); 5:47; 2:52; 2:47; 7:51; 4:37; 11:52

“Oh, no,” Paladin groaned. “Some of the clocks have been stolen!”

“How many?” chorused the rest of the Grey Labyrinth. Nobody could remember how many there were to begin with.

“You tell me,” Paladin smirked, knowing he had hit upon the final puzzle for the convention. “And, more importantly, tell me how you know.”

4. You are playing pool with the renowned pool shark, Saturated Fats. You know that he has some bizarre ideas about how you should arrange the balls in the rack. He has also been logging on to the Grey Labyrinth and is developing a taste for puzzles. “Tell you what,” Saturated Fats begins. “Let’s say that when you rack the balls, the score for any given ball is equal to the sum of the numbers on the balls touching the ball in question.” You roll your eyes. “The grand total,” he continues, “is the sum of the scores for all the balls. I want you to arrange the balls in such a way that you maximise the grand total.” You begin to arrange the balls. “And…” Saturated Fats adds, “Consecutively numbered balls can’t touch each other.” What is the highest grand total you can achieve by these rules?

5. When people don't want me, I take what they need. (If I'm lucky, they don't even notice.) When people wanted me, I took what they didn't need. But civilised people don't want me these days.

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