32 Arithmetic & Algebraic ProblemsThis appears to be an excellent method of introducing the elements of
algebra to the untutored mind. When the novice starts working it out he will
inevitably be adopting algebraical methods, without, perhaps, being conscious
of the fact. The two weighings show nothing more than two simultaneous
equations, with three unknowns.
- WEIGHING THE TEA
A grocer proposed to put up 20 Ibs. of China tea into 2-lb. packets, but his
weights had been misplaced by somebody, and he could only find the 5-lb.
and the 9-lb. weights. What is the quickest way for him to do the business?
We will say at once that only nine weighings are really necessary.- AN EXCEPTIONAL NUMBER
A number is formed of five successive digits (not necessarily in regular
order) so that the number formed by the first two multiplied by the central
digit will produce the number expressed by the last two. Thus, if it were
1 2 8 9 6, then 12 multiplied by 8 produces 96. But, unfortunately, I, 2, 6, 8, 9
are not successive numbers, so it will not do.103. THE FIVE CARDS
I have five cards bearing the figures
I, 3, 5, 7, and 9. How can I arrange
them in a row so that the number
formed by the first pair multiplied by
the number formed by the last pair,
with the central number subtracted,
will produce a number composed of
repetitions of one figure? Thus, in the
example I have shown, 31 multiplied
by 79 and 5 subtracted will produce2444, which would have been all
right if that 2 had happened to be
another 4. Of course, there must be
two solutions, for the pairs are clearly
interchangeable.- SQUARES AND DIGITS
What is the smallest square number that terminates with the greatest pos-
sible number of similar digits? Thus the greatest possible number might be