How many eggs in the basket
A women was carrying a basket of Eggs when a passer-by bumped her and she dropped the basket and all the eggs broke, Passer-by asked her number of eggs to pay her. Women replied, I don’t remember exactly , but I do recall that whether I divided the eggs by 2,3,4,5 or 6 there was always one egg left over. When I took the eggs out in groups of seven, I emptied the basket.
Can you tell, “How many minimum number of Eggs were there in the basket”?
See Solution
As in the previous problem we should find the least common multiple of 2,3,4,5 and 6 first, i.e. 60.
Now the the number of eggs can be 60+1, but its not completely divisible by 7.
So next possibility is 120+1, but its not completely divisible by 7 too.
So next possibility is 180+1, but its not completely divisible by 7 too.
So next possibility is 240+1, but its not completely divisible by 7 too.
So next possibility is 300+1, and its completely divisible by 7, so the minimum number of eggs in the basket should be 301.
Now the the number of eggs can be 60+1, but its not completely divisible by 7.
So next possibility is 120+1, but its not completely divisible by 7 too.
So next possibility is 180+1, but its not completely divisible by 7 too.
So next possibility is 240+1, but its not completely divisible by 7 too.
So next possibility is 300+1, and its completely divisible by 7, so the minimum number of eggs in the basket should be 301.
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301 Eggs
Multiple of 2,3,4,5,6 is the LCM of(2,3,4,5,6) = 60
Multiples of 60 Which is also multiple of 7 is 60*5 = 300 + 1 = 301
301/2 = Remainder is 1
301/3 = Remainder is 1
301/4 = Remainder is 1
301/5 = Remainder is 1
301/6 = Remainder is 1
301/7 = Remainder is 0
Nice one.
Thanks 🙂