A child fills his Easter basket with eggs during an Easter e

A child fills his Easter basket with eggs during an Easter egg hunt. When he returns to his parents, they divide them up into piles of 3 (one for each person) but have 2 left over. When grandma shows up, they divide them into piles of 4 and each person gets the same number. However, grandpa comes by and so they divide the eggs into piles of 5 and are left with one egg. They decide the goes to the child, so everyone is happy. What are all possible number of eggs that the child collected during the hunt?

Solution

Let the number of eggs be x,

now from question we can see that

1) x is of form (3a+2)

2) x is of form 4b

3) x is of form 5c+1

x= 3(a+2)4 = 4(b+1)4 = 5(c+1)4

Now, the smallest number which is divisible by 3,4,5 is lcm(3,4,5)=60

x will be of form 60 k-2

putting k = 1, x =56 is the minimum value of eggs ,it can be 56,116,176.236,...... (60k-4)