A rich man died. In his will, he has divided his gold coins among his 5 sons, 5 daughters and a manager. According to his will: First give one coin to manager. 1/5th of the remaining to the elder son.Now give one coin to the manager and 1/5th of the remaining to second son and so on….. After giving coins to 5th son, divided the remaining coins among five daughters equally.All should get full coins. Find the minimum number of coins he has?

2 Answers on this Question

1. Answer: 3121 gold coins
   Let total no of coins be M
   Let the disbursement D to each son:

   D1 = 1 + (M – 1)/5 = (M + 4)/5
   D2 = 1 + ( M – D1 -1)/5 = (D1) * 4/5
   D3= (D2) * 4/5
   D4= (D3) * 4/5
   D5= (D4) * 4/5
   Total disbursements to sons=
   = ∑D= (M+4)*1/5[ 1+4/5+(4/5)(4/5)+ (4/5)(4/5)(4/5)+(4/5)(4/5)(4/5)(4/5) ]
   = (2101/3125)*(M+4)
   Thus balance left for daughters =M-{(2101/3125)*(M+4)}
   =(1024M-8404)/3125
   This balance should be a positive integer ( assuming M and all disbursements are full coins )
   Thus 1024M-8404 should be a multiple of 3125….so….
   1024M – 8404 = N*3125 where N is an integer
   Using Python code:
   n=int(input(“Enter num n: “))
   X=int()
   a=int()
   a=0
   X=’ ‘
   for a in range(0,n+1):
   a=a+1
   X= (3125*a + 8404)/1024
   if (3125*a + 8404)% 1024== 0:
   print(X,a)
   Enter num n: 10000
   3121.0 1020
   6246.0 2044
   9371.0 3068
   12496.0 4092
   15621.0 5116
   18746.0 6140
   21871.0 7164
   24996.0 8188
   28121.0 9212
   We get minimum value of N = 1021 and M = 3121 gold coins

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   1. Correct last line in previous post. Minimum value of N = 1020

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