Problem 032

[alabax]

The problem statement seems unclear to me.

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

Where

n-digit number is pandigital if it makes use of all the digits 1 to n exactly once

Looks like it is asked to find sum of products from 1-digit, 2-digit, 3-digit, ..., 9-digit pandigital numbers satisfying the problem statement when only 9-digit numbers should be considered.

[rayfil]

The problem states (without the underline):

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

If you examine the given example 39 × 186 = 7254, the multiplicand/multiplier pair is 39 and 186. The product is 7254. The latter would be part of the required sum, not all the 9 digits. However, the total number of digits in the multiplicand, multiplier and product must be exactly 9 and those digits must be 1 through 9 pandigital.

[alabax]

It's clear that it is asked to find sum of products.

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

It's unclear that all identities should be 9-digit pandigital. Looks more like all pandigital identities with lengths 1 through 9 should be considered.

[jaap]

It's clear that it is asked to find sum of products.

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

It's unclear that all identities should be 9-digit pandigital. Looks more like all pandigital identities with lengths 1 through 9 should be considered.

But the phrase "1 through x pandigital" is used several times in the problem description, not just that last question. It is absolutely clear from the context there what it means:

for example, the 5-digit number, 15234, is 1 through 5 pandigital.

the identity, 39 × 186 = 7254, [...] is 1 through 9 pandigital.

[alabax]

Right, I should be more attentive.

[suitti]

Remember, the word product means the answer you get from multiplying.

In grade school, i thought i was good at word problems. But it wasn't until teaching my son how to get through them that i discovered how it is that i do them. Apparently, i think of lots of interpretations, pick one that seems most likely, then refine it as needed.

So, now i hear myself saying things like "product means multiply", "quotient means division", "difference means subtraction". He was doing gcf and lcm recently, and sure enough, there are wording cues there too. If they taught this explicitly in school, i missed it. They might have. They're not in my son's books.

It seems obvious now. But in grade school, definitions were things you had to memorize for tests, and then you could forget them. They seldom were used. It reminds me of the incredibly exciting Goblin Wars, and how professor Binns made the whole subject so boring.

I still have an ingrained dislike for definitions. I work in an industry where there are tons of brand new terms. Often there are three or four terms that mean the same thing, or a term that different people claim to mean quite different things. I often find myself translating. Certification exams often depend on them heavily.

Anyway, i'm getting to a level of problems here where my old approach simply doesn't work. Time for a new approach. Simply adding a "back track and try another interpretation" step is getting old.

[Lord_Farin]

I still have an ingrained dislike for definitions. I work in an industry where there are tons of brand new terms. Often there are three or four terms that mean the same thing, or a term that different people claim to mean quite different things. I often find myself translating. Certification exams often depend on them heavily.

This is why in mathematics, usually all important definitions are included for reference in a research paper. The ambiguity should be avoided to attain clarity. However such does not mean that definitions are irrelevant. They are, in my opinion, a backup whenever the intuition fails or the term has not settled in my brain. This all of course from a mathematical point of view.

[smythie86]

I have what I believe to be the answer for this problem, but it says it is invalid. Therefore, I must be missing something. I have 5 unique pandigital products that I believe satisfy all the requirements. Am I missing more? The possible combinations that I can think of to check are:

2 digit x 3 digit = 4 digit
1 digit x 4 digit = 4 digit

I can't think of any other possible combinations that would result in 9 total digits.

Are all of the products 4 digit numbers?

[jaap]

The answer to both your questions is yes.

[purpurato]

After several failed attempts at solving this problem, i decided to look for the answer somewhere. It appears to me that I found some other solutions that are not stated on the answer given. I double checked and still I think my solutions include more pandigital products. There might be some wording missunderstanding.
Can I send you my remarks via mail ?

[kenbrooker]

Can I send you my remarks via mail ?

Happy to try to help...

[hk]

After several failed attempts at solving this problem, i decided to look for the answer somewhere. It appears to me that I found some other solutions that are not stated on the answer given. I double checked and still I think my solutions include more pandigital products. There might be some wording missunderstanding.
Can I send you my remarks via mail ?

Please don't start a new topic for a problem if there already exists one.
Now I had to take the trouble to merge the two.