Something To Think About: Two Mathematical Thought Problems From Russia

The Russians have a long tradition of mathematical thought problems which occupies a distinguished part of their elementary mathematics classes.  Here are two samples by J. I. Pearlman:

  1.  Who Counted More?  Two people counted the number of people that passed them on the sidewalk for a period of one hour.  One stood at the gates of a house, the other walked up and down the sidewalk.  Who counted more?
  2.   The Grandfather and his Grandson.  What I am going to tell you took place in 1932.  My age then was the same as the last two digits of the year I was born.  When I told my grandfather about this correlation, he surprised me by declaring that the same correlation was true for his age as well.  How old was each of us?

About Robert M. Weiss
From an early age, I've taken great pleasure in reading. Also, I learned to play my 78 player when I was quite young, and enjoyed listening to musicals and classical music. I remember sitting on the floor, and following the text and pictures of record readers, which were popular in the 1940s and 50s. My favorites were the Bozo and Disney albums. I also enjoyed watching the slow spinning of 16s as they spun out tales of adventure. I have always been attracted by rivers, and I love to sit on a boulder with my feet in the water, gazing into the mysteries of swirling currents. I especially like inner tubing on the Rogue River in Southern Oregon. Since my early youth, I've been interested in collecting minerals, which have taught me about the wonderful possibilities in colors and forms. Sometimes I try to imagine what the ancient Greeks must have felt when they began to discover physical laws in nature. I also remember that I had a special passion for numbers, and used to construct them out of stones. After teaching Russian for several years, I became a writer, interviewer, editor, and translator. I continue to delight in form, and am a problem solver at heart.

2 Responses to Something To Think About: Two Mathematical Thought Problems From Russia

  1. berlioz1935 says:

    to 2: This is the easier one. You only need to divide the digits by two. In the case of the grandson, it is 32/2 = 16. He is born in 1916 and was 16 in 1932. The grandfather is 66! If you divide 132 by 2 and get 66. The extra hundred you get because you passed into a new century.

    to 1: this is a bit more problematic and is the same problem with the rain. Are you getting wetter walking towards the rain or standing in the rain for the same time?

    There are too many variables. For instance how fast the person is walking or will the people the walker encounters pass the gate where the other person is counting.

    There is nothing in the question whether the walker is moving at an equal speed at all time.

    Having read about the ‘rain-problem’ years ago, I seem to remember that it was said if the rain falls at a steady speed one encounter slightly more rain and, accordingly, slightly wetter.

    I’m not a mathematician and could not create a formula to solve the given problems mathematically.

  2. Thanks for sharing your insightful thoughts, Peter.

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