(2 votes, average: 5.00 out of 5)

## Project Euler Problem 33 Solution

#### Problem Description

The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.

We shall consider fractions like, 30/50 = 3/5, to be trivial examples.

There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator.

If the product of these four fractions is given in its lowest common terms, find the value of the denominator.

#### Analysis

This is curious problem and was able to solve it in just a few lines and 84 iterations. Just generated all fractions with 2 digit numerators and denominators and ignored ‘trivial’ examples. Used symmetry to consider distinct fractions – which was really not necessary, but…why not.

#### Solution

Runs < 1 second in Python.

```d = 1 for i in range(1, 10): for j in range(1, i): for k in range(1, j): ki = k*10 + i ij = float(i)*10 + j if (k*ij == ki*j): d *= ij/ki print "Answer to PE33 = ",d```

Added the float function to keep calculations from converting to integers.

## Discussion

### 8 Responses to “Project Euler Problem 33 Solution”

1. Nice solution Mike!

Posted by Rudy | February 17, 2011, 7:40 AM
2. Thanks, Rudy!

Posted by Mike | March 3, 2011, 1:29 PM
3. instead of (ij/ki == float(j)/k)
(k*ij == ki*j) is a better test, all integers.

Posted by Francky | April 29, 2011, 5:41 PM
4. faster again:
num = den = 1
for a in range(1,10):
for b in range(1,a):
q, r = divmod(9*b*a, 10*b-a)
if not r and q≤9:
num*=a
den*=b

Posted by Francky | May 19, 2011, 1:27 PM
5. i can’t understund why are you using “float”

when i delet it ,the solution become 80

Posted by Mellatora | January 28, 2012, 7:17 AM
6. In order to keep the math in floating point as Python defaults to integer and rounds the result from divisions.

Posted by Christner | January 30, 2012, 2:26 PM
7. Oh okey i understund it now
Thank so much :

Posted by Mellatora | February 1, 2012, 2:07 PM