Chickens

If a hundred chickens eat a hundred bushels of grain in a hundred days, how many bushels will ten chickens eat in ten days?
And if, on the average, one and a half of these chickens lay an egg and a half in a day and a half, how many days will it take a chicken to lay one and a half dozen eggs.

SOLUTION :

The tendency in the first problem is to conclude that if 100 chickens eat 100 bushels in 100 days, one chicken will eat one bushel in one day and any farmer will certainly quarrel with the likelihood of this calculation. The correct reasoning leads to this conclusion: if any number of chickens eat 100 bushels in 100 days, then the same number of chickens will eat one bushel in one day. This reasoning yields the correct answer 10 chickens will eat one bushel in 10 days.
The same process of reasoning leads to 27 days as the time required for one chicken to lay 1 1/2 dozen eggs.

Read More......

Ten Digits

1. Arrange the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 in succession using each one only once and, with the aid of plus and minus signs as desired, produce a sum of 100.
2. Add zero to the nine digits above and rearrange them in fraction form to produce a sum of 1.

SOLUTION :

1. 123-45-67+89=100
2. 35/70 + 148/296 = 1/2 + 1/2 = 1
The first answer appears to be unique, but there are numerous ways to rearrange the second answer.-QED-

Read More......