536 Puzzles and Curious Problems

242 Answers

SO. MEETING TRAINS

As the journey takes five hours, divide the route into five equal distances.

Now, when the lady leaves Wurzletown there are four trains on the way and

a fifth just starting. Each of these five she will meet. Also, when she has gone

one-fifth of the distance, another will start; at two-fifths, another; at three-

fifths, another; at four-fifths, another; and when she arrives at Mudville a train

will be just on the point of starting. If we assume, as we must, that she does

not meet this one "on the way," or meet the one that arrived at Wurzletown

just as she left, she will have met altogether nine trains on the journey.

81. CARRYING BAGS

Let the boy continue to carry one bag for I \-) miles; then hand it to the

gentleman, who will carry it to the station. Also let the man carry his bag 27'3

miles and then deliver it to the boy, who will carry it for the remaining

distance. Then each of the three persons will have carried one bag 27'3 miles

-an equal division of labor.

82. THE ESCALATOR

Let n equal the number of steps in staircase, and take as the unit of time the

time taken by one step to disappear at bottom.

The second man takes 75 steps in n - 75 units of time, or (dividing by 25)

3 steps in n 2575 units. Therefore first man takes I step in n 2575 units. But

fir st man al so takes (^50) steps ill. n - 50' uruts 0 f' tlllle, or I step ill. ---so n -^50 umts.
of time. Therefore n 5050 = n 2575 and n = lOO-the required answer.

83. THE FOUR CYCLISTS

A, B, C, D could ride one mile in Ii, Y9, VI2, and llI5 of an hour respectively.
They could, therefore, ride once round in Y18, ~7, -)6, and \45 of an hour, and
consequently in V9 of an hour (that is, 67'3 minutes) they would meet for the
first time. Four times in 67'3 minutes is 267'3 minutes. So that they would com-
plete their task in 26 minutes 40 seconds past noon.