268 Answers46,368, and if we add all the twenty-five terms or years together we get the
result, 121,392, as the correct answer. But we need not do that addition.
When we have the twenty-fourth and twenty-fifth terms we simply say (46,368
multiplied by 2) plus 28,657 equals 121,393, from which we deduct 1.
- SUM EQUALS PRODUCT
If you take any number in combination with 1 and a fraction whose numer-
ator is 1 and its denominator 1 less than the given number, then the sum and
product will always be the same. Thus, 3 and 1 Y.J, 4 and 1 Y.J, 5 and 114, and so
on. Therefore, when I was given 987654321, I immediately wrote down
1 9876~4320 and their sum and product is 987654322 9876~4320
Now, the reason why 2 and 2 are often regarded as an exceptional case is
that the denominator is 1, thus 2 and I VI, which happens to make the second
a whole number, 2. But it will be seen that it is really subject to the universal
rule. A number may be fractional as well as whole, and I did not make it a
condition that we must find a whole number, for that would be impossible
except in the case of 2 and 2. Of course, decimal fractions may be used, such
as 6 and 1.2, or 11 and 1.1, or 26 and 1.04.
In short, the general solution is n added to or multiplied by
n I
--I n- = (n + 1) + --1· n-- SQUARES AND CUBES
The solution in the smallest possible numbers appears to be this:102 - 62 = 100 - 36 = 64 = 43 •
103 - 63 = 1,000 - 216 = 784 = 282 •- CONCERNING A CUBE
(1) 6 feet. (2) 1.57 feet nearly. (3) Y36 foot.