An egg vendor calls on his first customer, and sells half of his eggs and half an egg.
To the second customer, he sells two-thirds of what was remaining and one-third of an egg.
To the third customer, he sells three-fourths of what was remaining and one-fourth of an egg.
To the fourth customer, he sells four-fifths of what was remaining and one-fifth of an egg

The vendor had precisely three eggs at the end of the fourth transaction.

The total number of eggs at the beginning was a whole number. No broken eggs were sold nor were any egg broken in between any two steps or after the last step.

How many eggs did the egg vendor start with?

By inspection:

Start with 395 eggs 395*1/2 = 197+1/2    
Sell 197+1/2+ 1/2 = 198 leaving 197    
2/3*197=131+2/3     
Sell 131+2/3+1/3 = 132 leaving 65    
3/4*65=48+3/4    
Sell 48+3/4+1/4=49, leaving 16    
4/5*16 = 12+4/5    
Sell 12+4/5+1/5=13, leaving 3, as was required  

Edited on December 28, 2015, 9:48 am

Posted by broll on 2015-12-28 09:24:13