Caught in the act: The Wknd Puzzle by Dilip D’Souza

He’s playing games, breaking hearts, leaving a trail of clues. Maybe you can guess what train Mahesh is on, but he’ll never guess who’s waiting.

Mahesh lives in Bandra. One day before the first Covid lockdown, he planned an evening out with a girlfriend. A devious sort, he had two girlfriends, both of whom live near Churchgate. Being puzzlingly devious, he set them both a brain-twister; whoever first solved it and turned up to meet him would have the pleasure, or otherwise, of his company.

He told girlfriend #1, Saumya, the hour that the train he was going to catch left Bandra for Churchgate. He told girlfriend #2, Marzia, the minute of the hour it left Bandra. (So if it was an 1135 train, for example, he would have told Saumya “11” and Marzia “35”). He also told them he would catch a train between 1400 and 1800.

Now Saumya and Marzia happen to know each other. And they like puzzles. That day, they consulted the Western Railway timetable and found that in those four hours, ten trains left Bandra for Churchgate, at these times: 1427, 1436, 1448, 1503, 1539, 1608, 1627, 1703, 1708 and 1748.

Saumya said to Marzia: “I have no idea when his train leaves Bandra, and I know you don’t either.”

Marzia said: “You’re right, I didn’t know. But now I do!”

Saumya said: “Hey! Now I know too!”

And together, they decided they’d had enough of Mahesh’s puzzles and his two-timing, and that neither of them would meet him at Churchgate that day. Or in fact, ever again.

Spare no sympathy for Mahesh arriving at Churchgate to find no girlfriend waiting. But when did his train leave Bandra?

Scroll down for the answer.

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Answer:

Think of Saumya’s first statement. If Mahesh has told her “14”, she knows that Marzia must have “27”, “36” or “48”. With either “27” or “48”, Marzia would not know which train — for there’s a 1427 as well as a 1627, and a 1448 as well as a 1748. But if Marzia had “36”, she would know Mahesh’s train for sure: the 1436 (no other train leaves at 36 past the hour).

That is, if Saumya has “14”, she cannot be sure that Marzia doesn’t know the train. Yet Saumya is sure Marzia doesn’t know the train. Thus Saumya can’t have “14”.

The same applies to “15”, eliminating it as well for Saumya.

But with “16”, Marzia would have either “08” or “27” and both are repeated (1608 and 1708, 1627 and 1427). Similarly with “17” (1703 and 1503, 1708 and 1608, 1748 and 1448). So because of her first statement, Saumya’s number must be either “16” or “17”.

Thus Marzia’s number is “03”, “08”, “27” or “48”, and she knows it must be one of the 16xx or 17xx trains. But she can’t have “08” — because then she would not be able to choose between 1608 and 1708. Since she says she now knows which train it is, she must have one of “03”, “27” or “48”.

Back to Saumya, whose number is either “16” or “17”. If “17”, she would still not be able to decide, because it could be either 1703 or 1748. But she now announces that she knows the train. Thus she must have “16”, and thus Mahesh’s train is the 1627.