Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
FoolForMath
Group Title
Just another cute problem:
Suppose \(xyz\) is a three digit number such that \(xzy + yxz+yzx+zxy+zyx = 3024\), then can you find \(x
\times y \times z\)?
 2 years ago
 2 years ago
FoolForMath Group Title
Just another cute problem: Suppose \(xyz\) is a three digit number such that \(xzy + yxz+yzx+zxy+zyx = 3024\), then can you find \(x \times y \times z\)?
 2 years ago
 2 years ago

This Question is Closed

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
XYZ = 100x + 10y + z Is it something related to this?
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Could be, my approach is somewhat different.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
100x + 10z + y + 100y + 10x + z ...... = 3024
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
let me think
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
122x + 212y + 221x = 3024 I can't go any further :?
 2 years ago

cwtan Group TitleBest ResponseYou've already chosen the best response.0
need Permutation?
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
@cwtan: I used permutation.
 2 years ago

karatechopper Group TitleBest ResponseYou've already chosen the best response.0
what is permutation
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Hmm...I'm not sure which permutation to use here.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Number of arrangement.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Number of arrangements if order matters.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
As far as I know, you used permutations only to arrange xyz in different ways
 2 years ago

karatechopper Group TitleBest ResponseYou've already chosen the best response.0
i think im gettting to it!!
 2 years ago

karatechopper Group TitleBest ResponseYou've already chosen the best response.0
wait..whats the permutation formula?
 2 years ago

karatechopper Group TitleBest ResponseYou've already chosen the best response.0
ffm...http://www.mathwords.com/p/permutation_formula.htm in this liinik what do the dots mean in the formula
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Permutations formula: \(\Large \color{Black}{\Rightarrow _nP_r = {n! \over (n  r)!} }\)
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
... this is not a straight forward permutation problem.
 2 years ago

karatechopper Group TitleBest ResponseYou've already chosen the best response.0
can u give me a hint..
 2 years ago

cwtan Group TitleBest ResponseYou've already chosen the best response.0
I like this question when i am unable to solve it......
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.3
is the answer:\[x\times y\times z = 126\]?
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Yes, approach? :)
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.3
very weird, im pretty sure its nowhere near the best way to look at this.
 2 years ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.1
222 * 18  3024 = 972  Whose sum of digits = 18 too.
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.3
Note that 3024 is divisible by 9. Also note that if the three digit number xyz leaves a remainder of r when divided by 9, that any permutation of the digits must leave the same remainder. So adding up those 5 permutations will leave 5r as a remainder. Hence we have this equation:\[5r \equiv 0 \mod 9\]the only solution to this is r = 0 , so the number xyz is divisible by 9, which means the sum of its digits is divisible by 9. Now use what siddhantsharan posted above, using the fact that x+y+z can only be 0, 9, 18, or 27. Its guess and check from there.
 2 years ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.1
Actually the above post by joemath shortens it down to only 18. As x + y + z must be 15 at least For it to be > 3024. And 222*27  3024 will obviously not leave a 3 digit no. Hence 18 has to be correct. Without any guess and check.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Interesting approach can we generalize it?
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Why do you choose divisibility by 9 in the first place?
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.3
because of how divisibility by 9 is sorta tied to the digits of the number. You can find a numbers remainder when you divide by 9 by adding the digits together. it seemed like a lucky break that 3024 was divisible by 9.
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.3
hmm...actually i take that back, the problem will still be doable even if that sum wasnt divisible by 9. Since we are adding 5 numbers, we will always be able to solve the equation:\[5r\equiv k \mod 9\]Since 5 is invertible (mod 9).
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.3
where k is the remainder of the sum after division by 9.
 2 years ago

cwtan Group TitleBest ResponseYou've already chosen the best response.0
So the answer is ? 126?
 2 years ago

karatechopper Group TitleBest ResponseYou've already chosen the best response.0
i googled and got 126 but at first when i was solving problem i thought i had to find out what x y and z were..
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.