Maths riddle

I

IamChris

New member
Joined
Sep 21, 2015
Messages
5
Hi folks

I have been asked to find an answer to a riddle that has me beaten.

What number (N), when multiplied by 99 results in an answer with a number 1 at the beginning and a 1 at the end.

Any help appreciated.

sorry but I forgot to add the important bit, the resulting number must contain the number (N) in the middle. Ie 1 N 1
 
Last edited:
IamChris said:
Sorry Denis, I made a mistake now edited.
Click to expand...

You saw Denis's answer to your incomplete post.

That should give an idea about how to tackle this problem!

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting
 
I did read the read before posting but don't have any working out to post.

I'm afraid I don't know how to tackle the problem, do you ?

chris


Subhotosh Khan said:
You saw Denis's answer to your incomplete post.

That should give an idea about how to tackle this problem!

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting
Click to expand...
 
You may not know anything about the number N, but you do know somethings about 99N. Begin by listing multiples of 99. What do you notice about the first digits? Can you predict for which values of N, 99N will begin with the digit 1? Similarly, what do you notice about the last digits of the multiples of 99? Can you predict for which values of N, 99N will end with the digit 1? Can you then put those two pieces of information together and determine for which values of N, 99N both begins and ends with the digit 1? Once you've narrowed down the possible values of N, ​try and find the smallest value which is in the form, as you call it, 1 N 1.
 
Denis said:
u = LEN(n) : length of n

n = [10^(u+1) + 1] / 89

Found 2 integer solutions: one has u=21 digits, next has u=65 :shock:

The 65 digits n: 1 112359........752809 1 : total 67 digits with the 1's

Not sure if I'm allowed to give you the 21 digits solution;
is this for a competition?

What u tink, Subhotosh?
Click to expand...

not a competition just a bit of fun.
 
IamChris said:
not a competition just a bit of fun.
Click to expand...

Well - then - you know the answer/s exist and you know the equation from which the answer came.

To complete your fun, now you can calculate the rest of the digits.

After a week (just in case it was a competition), Denis might provide you the answer (after having coffee and his beauty-nap as he feels less cranky).
 
You must log in or register to reply here.
Top