Project Euler Forum

Hello all,

I have trouble understanding how to submit the answer to problem 33. I have the 4 non-trivial fractions, written in the same way as the example (49/98). What is meant by "the product of these four fractions is given in its lowest common terms" ? If a1/b1, a2/b2, a3/b3 and a4/b4 are the four fractions, does that mean the answer should be lcm(b1, b2, b3, b4) ? (tried it, it doesn't work).

Thanks for your help !

consider 2/5*10/13=4/13
Is the denominator lcm(5,13)=65?

If a1/b1, a2/b2, a3/b3 and a4/b4 are the four fractions, you should multiply all four fractions:
(a1*a2*a3*a4) / (b1*b2*b3*b4)
simplify this fraction, and then give the denomitor (the number you're dividing by)

Thank you both, I was so focussed on the denominator that I din't even look at the numerator

Hi, I'm also puzzled by how to submit this answer, notwithstanding the above.

My program found the four fractions, one of which is 49/98, and I verified manually that the others are correct. The product of the fractions is snip . I reduced this to lowest common terms by dividing the numerator and denominator by snip, yielding snip. As I read the question and comments above, the answer is snip. This is is rejected. Is this a calculation error on my part, or am I using the wrong process?

Edited away spoilers.
Please don't post answers (or attempts to answers).
You did not divide out all common factors. Nominator and denominator still have a common factor.

Sorry, thanks! I shouldn't be doing these at 1 AM.

I dont exactly understand the difference between trivial and non-trivial examples. Can anyone guide me please.

Trivial examples are (10*a)/(10*b), where you simplify by deleting the zeros.
Nontrivial examples are such where simplification is "achieved" by deleting the same nonzero digit from numerator and denominator, like the given example 49/98 where you delete the 9 from numerator and denominator and obtain the simplified fraction 4/8.

daniel.is.fischer wrote:Nontrivial examples are such where simplification is "achieved" by deleting the same nonzero digit from numerator and denominator, like the given example 49/98 where you delete the 9 from numerator and denominator and obtain the simplified fraction 4/8.

In that case, there will be many non-trivial examples and not just 4 like 48/86, 34/47, 57/76, 77/79, 18/86, etc.

I think I didn't get what you were trying to say. Can u clarify it a bit more?

mahendrakariya wrote:In that case, there will be many non-trivial examples and not just 4 like 48/86, 34/47, 57/76, 77/79, 18/86, etc.

The difference is that 49/98 really does equal 4/8. 48/86 does not equal 4/6.

Thanks. I got it.

Hello.

I was stuck for the same reason. I think the description of the problem is not very accurate.

The term 'trivial example' is not really defined, it is only presented through an example.
Additionally, there are two constraint that hold for the correct solution:
1) the cancellation may not be trivial, (i.e. cancellation of the 0, which is not clearly explained)
2) the improper (cancellation of single digits) cancellation must coincide with the proper cancellation (cancellation of common divisors)

I think the reason for my confusion was the fact that both constraints were not clearly enough defined.

Normally the task descriptions in Project Euler are spot-on, so maybe someone can correct this little lapse?

Thanks for the great website anyway

Problem 33 text in chrome looks like this:

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

We shall consider fractions like, to the power of 30/ subscript 50 = to the power of 3/ subscript 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.

Please try to fix it, i had to open it in firefox to understand the problem. This is very confusing.

If Chrome doesn't understand the ordinary html sequence ⁴⁹/₉₈ I think Chrome should be fixed rather than our website.

While this should probably be moved to another forum, it is really more of a problem with the site - I presume the CSS was updated to include hiding <span class="hidden">..</span> but everyone's CSS is still cached (I normally add ?a=1 or something when changing CSS to force it to update for everyone).

Of course, one refresh fixes the problem, but the 'hidden' text makes no sense on this particular problem.

(Also explains viewtopic.php?f=50&t=2281)

I had completed and revisited question 33 recently and had attempted to redo it. I had realized that the question needed to be reworded inorder for one to better understand the meaning of the term a non-trivial number. Additionally, in that sense, the use of the term a curious number seemed to make no sense to me at all as for it seemed to be (though it is not) irrelevant to the term non-trivial number. I feel that it should be reworded and I am posting this inorder to get the attention of the administrators. Though I primarily received the right answer, I was questioning myself as for why the fraction 11/55 was not considered a non-trivial number. This number, like all those in the correct answer, was a curious number in that both 11/55 and 1/5 were both equal to 0.2

ngahlot wrote:Though I primarily received the right answer, I was questioning myself as for why the fraction 11/55 was not considered a non-trivial number. This number, like all those in the correct answer, was a curious number in that both 11/55 and 1/5 were both equal to 0.2

11 had no digits in common with 55, so it is not possible to do this curious cancellation of the same digit from numerator and denominator.

Also, please don't start a new topic when a thread for the problem already exists.

@@ngahlot

We realize you are new to this forum. For your information, if you need to post anything related to the Euler problems, You will find them listed as "Problem XXX" with the number padded with leading 0's to get a 3-digit number. Enjoy the site.

ngahlot wrote: the question needed to be reworded inorder for one to better understand the meaning of the term a non-trivial number.

You have a point there -- "like, ³⁰/₅₀ = ³/₅" is not a great definition of trivial, although a large number of people have figured out that it means "a fraction reduced by canceling trailing zeros". Canceling equal numbers of trailing zeros in the numerator and denominator is actually a legitimate method of fraction reduction.