# math

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A farmer walks into a store and heads for the counter. On the counter is a basket of hard-boiled eggs. The farmer says to the cashier,"I'll take half of your eggs plus half an egg."
The next day he walks in the store and says to the cashier,"I'll take half of your eggs plus half an egg."
On the third day, the farmer walks into the store and says th the cashier,"I'll take half of your eggs plus half an egg." There are now no more eggs in the basket. How many eggs were there to begin with?

• math -

There were 3 eggs.

• math -

• math -

half of three eggs is 1.5, plus half an egg is 2 eggs, leaving one.

The next day, he takes half the egg, plus a half. That is all the eggs.

the third day, no eggs remain to get.

• math -

You could work backwards to get the answer.

On the third day, he bought half the egg(s) plus half an egg. There was nothing left.

That means that what was left plus half an egg was half of what was there after he bought half of the eggs.

Therefore before he walked in, there were:
2 × (0+1/2)
=1 egg

Same happened on the second day, so before he walked in, there were:
2 × (1+1/2)
= 3 eggs.

Same happened on the first day, so before he walked in, there were:
2 × (3+1/2)
= 7 eggs.

Remember, we have assumed that there were no more nor less eggs than what he bought, no one else bought the eggs, and he bought what was left there from three days ago (yuck!).

You can now start with 7 eggs and go through the scenario and see if it still works.

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