264 Answers- SELLING EGGS
The smallest possible number of eggs is 103, and the woman sold 60 every
day. Any multiple of these two numbers will work. Thus, she might have
started with 206 eggs and sold 120 daily; or with 309 and sold 180 daily. But
we required the smallest possible number.- PUSSY AND THE MOUSE
You have simply to divide the given number by 8. If there be no remainder,
then it is the second barrel. If the remainder be 1, 2, 3, 4, or 5, then that re-
mainder indicates the number of the barrel. If you get a remainder greater than
5, just deduct it from 10 and you have the required barrel. Now 500 divided
by 8 leaves the remainder 4, so that the barrel marked 4 was the one that
contained the mouse.- ARMY FIGURES
The five brigades contained respectively 5,670; 6,615; 3,240; 2,730; and
2,772 men. Represent all the fractions with the common denominator 12,012,
and the numerators will be 4,004; 3,432; 7,007; 8,316; and 8,190. Combining
all the different factors contained in these numbers, we get 7,567,560, which,
divided by each number in turn, gives us 1,890; 2,205; 1,080; 910; and 924.
To fulfill the condition that the division contained a "little over 20,000 men,"
we multiply these by 3 and have the correct total-21,027.
- A CRITICAL VOTE
There must have been 207 voters in all. At first 115 voted for the motion and
92 against, the majority of 23 being just a quarter of92. But when the 12 who
could not sit down were transferred to the other side, 103 voted for the
motion and 104 against. So it was defeated by I vote.
- THE THREE BROTHERS
Arthur could do the work in 143 %9 days, Benjamin in 172%1 days, and
Charles in 23'l31 days.