For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
03/09/2016

Problem 1
Two tourists visit the Dutch city of Gouda. During their tour through the center, they spot a cozy terrace. They decide to have a drink and, as an appetizer, a portion of hot "bitterballs" (bitterballs are a Dutch delicacy, similar to croquettes). The waiter tells them that the bitterballs can be served in portions of 6, 9, or 20. What is the largest number of bitterballs that cannot be ordered in these portions?

Problem 2

A swimmer jumps from a bridge over a canal and swims one kilometer stream up. After that first kilometer, he passes a floating cork. He continues swimming for half an hour, then turns around, and swims back to the bridge. The swimmer and the cork arrive at the bridge at the same time. The swimmer has been swimming with constant effort. How fast does the water in the canal flow?

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Problems from 2/25/16

Problem 1
How many times do the two hands of a clock point in the same direction between 6:00 am and 6:00 pm of a single day?

Problem 2
I woke up one night and heard my clock strike "one." I was too tired to turn on the light to see what time it was. As I lay there pondering, it occurred to me to speculate how long I would have to lie awake in order to be sure what was the exact time. My clock strikes the hours and strikes "one" each half hour. I fell asleep before I solved the problem, but can you work out what is the longest time I would have to lie awake after hearing the strike "one," to be sure of the time?

Congratulations to Avanish Gowrishankar, Amit Lele and RK Sambangi, who were the winners of last set of puzzles.

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