perplexus.info :: Just Math : Distinct Digit Determination II

Distinct Digit Determination II (Posted on 2010-12-15)

Each of A and B is a (base 15) positive integer , with A containing precisely 201 digits and, B containing precisely 202 digits, where:

A = 77…..779 (the digit 7 is repeated precisely 200 times followed by 9), and: B= 77…..779 (the digit 7 is repeated precisely 201 times followed by 9)

Determine the distinct digits in the base 15 representation of A². What are the distinct digits in the base 15 representation of B²?

*** For an extra challenge, solve this puzzle without the help of a computer program.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Manual Approach (spoiler)

Comment 2 of 2 |

2A (base 15) = 100..003 where there are precisely 200 zeroes.

4A²(base 15) = 100..00600..009 where there are precisely 200 zeroes between the 1 and the 6 and 200 more between the 6 and the 9.

I haven't checked, but I assume that dividing by 4 (base 15) gives Charlie's answer.

And a similar approach should suffice for B.

Posted by Steve Herman on 2010-12-16 16:27:38

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info