Problems Drive 1964
M. S. PATERSON AND MISS
J. E. HEARNSHAW
- Write down as many primes as you can which are palindromic (read
the same in both directions) in binary notation, e.g. 17 (=
- At noon precisely, a train leaves A for B, and another leaves B
for A. They pass after 51 minutes. Each train stays 27 minutes at
its destination and then returns by the same route. The trains from A
and B travel throughout with constant speeds of 23 m.p.h. and 39
m.p.h., respectively. At what time do they pass for the second
- (a) 3, 4, 6, 8, 12, 14, ... add two terms.
(b) 61, 52, 63, 94, 46, ... add one term.
(c) 1, 2, 3, 5, 16, 231, ... add one term.
(d) 65, 58, 72, 107, ... add one term.
- Your are given a 15-pint, a 10-pint and a 6-pint measure, and an
unlimited water supply. Find a method of obtaining exactly 1 pint in
each of two measures, using the fewest possible number of operations.
(Marking of measures is not permitted. An operation is either filling
or emptying one measure, or transferring water from one to
In the multiplication sum
the letters represent different digits in the scale of ten. If E =
4, what is (A + B + C + D)?
There are three uniform thin planks of lengths (and weights) 4,
3 and 2 units, respectively. In this diagram, they are arranged on
the edge of a shelf so as to project a distance of 2½ units
over the edge. How can they be rearranged to project the maximum
Solve the following cross-number puzzle (in integers in the
scale of ten).
where c is prime and a = 2c + d - 2b, b = (a2 +
c2)/2d, and d = (a - b)2 + c.
My friend tosses two coins and covers them with his hand. "Is
there at least one 'tail'?" I ask. He affirms this (a).
Just then he accidentally knocks one of them to the floor (b). On
finding the dropped coin under the table, we discover it to be a
"That is all right," he says, "because it was a 'tail' to start
At each point (a), (b), (c) and (d) of this episode I calculated
what, to the best of my knowledge, was the probability that both coins
showed 'tails' at the time. What were these probabilities?
Find the last digit of:-
3333377777 - 7777733333
- The planet Kophikkup is in the shape of a torus or ring-doughnut.
There is a direct mono-rail line from each of the four space-ports to
each of the major cities. No lines join or cross. What is the
greatest possible number of major cities? Draw a diagram for this
- I have a wire model consisting of the edges of a cube. If I
remove exactly three of the edges, how many different structures can I
- When my sister is four times as old as she was when I was twice as
old as my brother, my brother will be two-thirds as old as I will be.
My brother and I are teenagers; how old was my sister on her last
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