+0

# Multiple questions... please don't hate

+1
117
4
+55

Hi everyone! I am new here, and I have multiple questions.  One is a mathematics question, so I will put that first:

Find a base 7 three-digit number which has its digits reversed when expressed in base 9.

I understand that this is a homework question that some may recognize, but I am not trying to cheat.  I am only trying to get some hints in the right direction, and I will try to solve it with any replies.  I have posted a question as a guest, but the only reply I got was to not cheat.

My second question is regarding the website.  I posted an answer to someone's question on this forum, but I saw that it said that it has been flagged.  Does this mean another user has reported it, or is it just automatic for new users? I really don't want to get into any trouble...

Jun 18, 2020

#1
+111112
+3

Find a base 7 three-digit number which has its digits reversed when expressed in base 9.

Let the digits of the number be a,b,c where

a is between 1 and 6 inclusive and

b is between 0 and 6 inclusive

and

c is between 1 and 6 inclusive

a>c

\(49a+7b+c=81c+9b+a\\ 0=80c+2b-48a\\ 0=40c+b-24a\\ 24a-b=40c\\ \)

24a could be    24,  48,  72, 96,  120,  144

40c could be     40,  80,

I do not think I will finish it since it is obviously a challenge question for you. You need to examine all the possibilities in orger to find triplets that work. It is not as tiresome as it may seem.

When you finish it, it would be nice for you to display the rest, (or the alternate) logic that you use.

That is another challenge for you.

Please let Kitten continue this. Do not finish it for her. Thanks

LaTex:

49a+7b+c=81c+9b+a\\
0=80c+2b-48a\\
0=40c+b-24a

Jun 19, 2020
edited by Melody  Jun 19, 2020
#3
+55
+2

Hi! Thank you guys for responding.  I solved it!  I did it like this:

The base 7 number can be "abc_7", and a, b, and c are all digits from 1 to 6, except for b which can also be 0.  Then you can expand it to be 49a + 7b + c.  Then when it is reversed, you get cba.  expanding in base 9, cba_9= 81c+ 9 b + a.  The two expressionss are equal, so you can use the equation 49a + 7b + c = 81c + 9b + a.  Then you move everything to one side and get 80c + 2b - 48a = 0, and you can simplify and get 40 c+ b- 24a = 0.  Then we can solve for b and get  b   = 24a - 40c = 8(3a - 5c). This means that b is divisible by 8, but it is also a base 7 digit so it has to be 0.  then you have 3 a = 5c sp a is divisible by 5 and c is divisible by 3.  They cant be 0 because they are both left digits, so they are 5 and 3.  This means that the answer is 503_7.

Hooray!  Thank you again for helping me :)

ConfuzzledKitten  Jun 19, 2020
#4
+111112
+2

It is nice to see that you have finished for yourself ConfusedKitten.  Congratulations!

Melody  Jun 20, 2020
#2
+986
+1

If it's flagged, it means you may have put some offensive language... not that offensive, just use regular language and not rude ones, and don't put italics.

/

You aren't in trouble....

Hope melody has cleared your "confuzzledness"!

Jun 19, 2020