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#111 Eclair-voyance

Tom and Amy are colleagues who are both excellent logicians; they speak honestly and accurately, and no bit of good deduction slips past them. Another thing they won鈥檛 let slip past is the last eclair on the tray at the annual puzzlers鈥� party. Since neither is willing to back down, they propose a solution. They will take the spades out of a deck of playing cards and remove the ace, king, queen and jack, leaving them with the 2, 3, 4, 5, 6, 7, 8, 9 and 10 of spades. They will shuffle the remaining cards and each draw one. Whoever has the higher card gets the eclair.

They each take a card and look at it, being careful not to show it to the other.

鈥淲ell I don鈥檛 know whether I鈥檒l win,鈥� says Tom, 鈥渂ut I hope I do.鈥�

鈥淪ame goes for me,鈥� replies Amy.

鈥淒o you know who won yet?鈥�

鈥淣o,鈥� says Tom.

鈥淢e neither,鈥� says Amy.

At that, Tom sighs and tosses his card back into the deck, admitting defeat.

What cards did Tom and Amy have?

Solution next week

#110 Reflecting on time

Solution

It was 11:51 when I woke up. The only digits that reflect to make a valid digit are 0, 1, 2 and 5. Digit 8 would work for the second digit in the hours or minutes, but can鈥檛 be transposed to another position on the clock and give a legitimate time. The hour must change, and if it changes by 1, then it could be 01 to 02, 20 to 21 etc. The smallest time advance (apart from zero) turns out to be 20 minutes. There are three times when this happens: 01:50 (reflection 02:10); 11:51 (12:11) and 21:55 (22:15). Only one of these is in daytime 鈥� which is why the darkness of the tunnel made the difference.