## Concatenation puzzle: when (A || B) / B is an integer

Concatenation is the joining of two numbers by their numerals. That is, the concatenation of   444   and   777   is   444777.

Concatenation of numbers   A   and   B   is denoted   A || B.

A   and   B   are three-digit integers.   So   A || B   is a 6-digit number.

So, what is the smallest integer of the form   (A || B) / B ?

Note the trivial solution is :
A = 001,   B = 500,   then   A || B = 001500   and   (A || B)/B   =   001500/500   =   3 math grad - Interest: Number theory
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### 1 Response to Concatenation puzzle: when (A || B) / B is an integer

1. David a/k/a @InfinitelyManic says:

#!/usr/bin/python
# David a/k/a/ @InfinitelyManic
# Concatenation puzzle: when (A||B)/B is an integer

# import Fractions from fractions module
from fractions import *

# declare list sol[utions]
sol = []
# we are going to put the data in a file
f = open(‘results.txt’,’w’)
# create two (2) for loops using range. Range will end at 999, respectively.
for A in range(100,1000):
for B in range(100,1000):
# concat A & B; turn into an int then do the math
frac = Fraction(int(str(A)+str(B)),int(B))
# if the denominator is 1 then write “A,B, fraction form, and numerator” to text file
if frac.denominator == 1:
sol = [A,B,str(A)+str(B),’/’,B,frac.numerator]
f.write(str(sol)+’\n’)

# close the file
f.close()

# #########Linux Bash ##############
\$ sort -n -k6 -t, results.txt | less # using sort to sort numerator value within file to find target numerator value (i.e., smallest & largest)