Mathematical & Logical Puzzles -Q7

25. Another Escalator Puzzle

            There are very long escalators in some New York subway stations.  You don’t have to climb them since the moving steps will do the job for you.  However, two brothers have to get to a baseball game and are in a hurry, and so they run up the moving steps, adding their speed to that of the escalator. 

            The taller boy climbs three times as quickly as his little brother and whilst he runs up he counts 75 steps.  The little one counts only 50 steps.  How many steps has the visible part of this New York escalator?

26. The Ladder Against The Wall

             AB is a wall at right angles to the ground BC.  DFEB is a square box 4 feet on a side.  AFC is a ladder 20 feet long whose extreme ends touch the wall and the ground, and whose length rests on the corner of the box.  How far up the wall does the ladder reach?  (i.e. What is the length of AB?)

27. A Coin Puzzle

            The problem is to change the arrangement of twenty-cent and ten-cent coins shown in Figure 1 to that shown in Figure 2, in the smallest number of moves.

                The only move allowed consists of sliding a pair of touching coins, which must be one twenty-cent coin and one ten-cent coin, from one point on the imaginary base line (which of course is the same in both drawings) to another.  The coins must remain in contact throughout the move and may not be rotated during the move to reverse the order of the coins moved.  Gaps are allowed at the end of every move except the last.

28. The Dilemma Of A Racecourse Owner

            A racecourse owner wished to install photoelectric timing devices on his racecourse, such that any distance between 1000 metres and 31000 metres (in multiples of 1000 metres) could be timed.  The photoelectric devices were extremely expensive and so he wanted to purchase the fewest possible.

            It must be possible, by choosing any two sets of these devices, to time one of the desired distances between them.  What is least number that he requires, and how would they be set out?  Assume for the purposes of this puzzle that the racecourse is a circular one.

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