An old woman went to the market and a horse stepped on her basket and smashed her eggs. The rider offered to pay for the eggs and asked her how many there were. She did not remember the exact number, but when she had taken them two at a time there was one egg left, and the same happened when she took three, four, five, and six at a time. But when she took them seven at a time, they came out even. What is the smallest number of eggs she could have had?
We have LCM(2,3,4,5,6)=60
THEN, we have the no. of eggs having the form 60*t+1
Since the no. of eggs is divisible by 7, we must have:
60*t+1 == 0(mod 7)
=> 4*t+1==0(mod7)
=> 4*t == -1 (mod 7) == 20 (mod 7)
=> t== 5 (mod 7)
The minimum value of t is 5, giving:
the required minimum no. of eggs as: 60*5+1= 301
Edited on June 9, 2022, 1:15 am
Puzzle Solution
