2 3 4 5 6 7 8 9 = 100.

It is required to place arithmetical signs between the nine figures so
that they shall equal 100. Of course, you must not alter the present
numerical arrangement of the figures. Can you give a correct solution
that employs (1) the fewest possible signs, and (2) the fewest possible
separate strokes or dots of the pen? That is, it is necessary to use as
few signs as possible, and those signs should be of the simplest form.
The signs of addition and multiplication (+ and x) will thus count as
two strokes, the sign of subtraction (-) as one stroke, the sign of
division (/) as three, and so on.

95.--THE FOUR SEVENS.

[Illustration]

In the illustration Professor Rackbrane is seen demonstrating one of the
little posers with which he is accustomed to entertain his class. He
believes that by taking his pupils off the beaten tracks he is the
better able to secure their attention, and to induce original and
ingenious methods of thought. He has, it will be seen, just shown how
four 5's may be written with simple arithmetical signs so as to
represent 100. Every juvenile reader will see at a glance that his
example is quite correct. Now, what he wants you to do is this: Arrange
four 7's (neither more nor less) with arithmetical signs so that they
shall represent 100. If he had said we were to use four 9's we might at
once have written 99+9/9, but the four 7's call for rather more
ingenuity. Can you discover the little trick?

96.--THE DICE NUMBERS.

[Illustration]

I have a set of four dice, not marked with spots in the ordinary way,
but with Arabic figures, as shown in the illustration. Each die, of
course, bears the numbers 1 to 6. When put together they will form a
good many, different numbers. As represented they make the number 1246.
Now, if I make all the different four-figure numbers that are possible
with these dice (never putting the same figure more than once in any
number), what will they all add up to? You are allowed to turn the 6
upside down, so as to represent a 9. I do not ask, or expect, the reader
to go to all the labour of writing out the full list of numbers and then
adding them up. Life is not long enough for such wasted energy. Can you
get at the answer in any other way?

VARIOUS ARITHMETICAL AND ALGEBRAICAL PROBLEMS.

"Variety's the very spice of life,
That gives it all its flavour."

COWPER: _The Task._

97.--THE SPOT ON THE TABLE.

A