Problem 032

friol · Post by **friol** » Sun Apr 20, 2008 11:44 am

Hello.
I think I've found the solution to problem 32, but projecteuler.net rejects it.

Problem 32 asks:
"Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital. "

I think these are the products:

[edit]Removed correct solution set[/edit]

and the sum of the products is _____, but it does not seem to be the answer.
What I'm doing wrong?

Thanks

euler · Post by **euler** » Sun Apr 20, 2008 11:54 am

I've edited your post to remove the list, as it is correct. Remember, the word product means the answer you get from multiplying. You might find the hint in the problem statement helpful.

friol · Post by **friol** » Sun Apr 20, 2008 11:59 am

Now I've got it 8-D
Thanks.

euler · Post by **euler** » Sun Apr 20, 2008 12:00 pm

You're welcome, and congrats.

vzhilyaev · Post by **vzhilyaev** » Fri Oct 17, 2008 2:54 pm

Am I getting it right that multiplicand/multiplier/product should have in total exactly nine digits?

daniel.is.fischer · Post by **daniel.is.fischer** » Fri Oct 17, 2008 3:18 pm

marco6 · Post by **marco6** » Tue Nov 25, 2008 11:55 am

can anyone explain me what does "pandigital" mean?
thanks

Georg · Post by **Georg** » Tue Nov 25, 2008 12:10 pm

Problem 41 (View Problem): We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once.

euler · Post by **euler** » Tue Nov 25, 2008 6:14 pm

Good question, marco6. I hadn't realised that a definition was missing from that question. I've added the same definition from problem 41 (thanks, Georg) as an introduction to the problem.

Problem 32 (View Problem)

marco6 · Post by **marco6** » Wed Nov 26, 2008 12:28 pm

Thank you for your answer!

Sunhill · Post by **Sunhill** » Sat Feb 07, 2009 11:54 pm

Mods: A very small typo in the last word of the first paragraph - "pandigitial".

daniel.is.fischer · Post by **daniel.is.fischer** » Sun Feb 08, 2009 12:54 am

Thanks - fixed.

masteusz · Post by **masteusz** » Fri Jan 21, 2011 12:43 pm

Hello,
I think that I have found correct solution but ProjectEuler rejects it so I have a question:
For example is 39 x 186 = 7254 and 186 x 39 = 7254 counted as one or two different pandigital identities?

jaap · Post by **jaap** » Fri Jan 21, 2011 2:29 pm

One. The problem clearly states:

HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.

Note that this is even stricter than just swapping the two factors.

masteusz · Post by **masteusz** » Thu Feb 03, 2011 8:11 am

Thanks, I omitted the word "once" while I was reading

jhughes · Post by **jhughes** » Sun Feb 27, 2011 4:36 am

Could someone explain to me what this problem is referring to by "identity"? I know it's meaning in other contexts, not this one.
Thanks in advance!

rayfil · Post by **rayfil** » Sun Feb 27, 2011 6:12 am

When you have an equal sign (=), it means that both sides must be considered identical. Thus, 39 × 186 can be considered an identity of 7254. Similarly 78 x 93, 31 x 234 and 13 x 18 x 31 would also be considered identities of 7254 among many others.

Spura · Post by **Spura** » Tue Jun 14, 2011 6:09 pm

Do we have to consider solutions with multiple multiplicands?
X * Y * Z = U

?

hk · Post by hk » Tue Jun 14, 2011 8:38 pm

Spura wrote:Do we have to consider solutions with multiple multiplicands?
X * Y * Z = U

?

No

Molx · Post by **Molx** » Tue Jun 14, 2011 8:47 pm

Spura wrote:Do we have to consider solutions with multiple multiplicands?
X * Y * Z = U

?

No, only Multiplicand * Multiplier = Product
Problem 32 (View Problem)

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