Irrational Base

By Susam Pal on 11 Sep 2007

Yesterday, I was going through Google's blog on their plans for Code Jam. I found an error in a document linked to from their blog post. I wrote an email to inform them about it. A few hours later, I got an amusing reply from them. Read the conversation below.

From: "Susam Pal"
To: Programmingcontest-feedback [at] google [dot] com
Date: Tue, Sep 11, 2007, 11:45 AM IST
Subject: Sample output of Problem A probably incorrect

I was going through this PDF file: http://services.google.com/blog_resources/Google_CodeJam_Practice.pdf.

Shouldn't the sample output for Problem A be 17 × 3 = 51? The sample output is mentioned as 120 which is incorrect. Please let me know what you feel.

Regards,
Susam Pal

From: "Bartholomew Furrow"
To: "Susam Pal"
Cc: Programmingcontest-feedback [at] google [dot] com
Date: Tue, Sep 11, 2007, 11:29 PM IST
Subject: Re: Sample output of Problem A probably incorrect

Susam,

If you write the answer in base 6.21110255, I think you'll find that 120 is correct.

You're quite right: that was the answer to another example (one that we did not use). We will push a fix shortly to the PDF, and we will have a much more careful review process for actual competitions.

Thanks for your careful attention,
Bartholomew

From: "Susam Pal"
To: "Bartholomew Furrow"
Cc: Programmingcontest-feedback [at] google [dot] com
Date: Wed, Sep 12, 2007, 12:04 AM IST
Subject: Re: Sample output of Problem A probably incorrect

Thanks for the quick response.

> If you write the answer in base 6.21110255, I think you'll find that > 120 is correct.

:-) Or base -8.2111025509. :-P

Regards,
Susam Pal

If you are wondering, how weird the numeral system must be in an irrational base or negative base, here's a surprise: Donald Knuth has worked on transcendental base and imaginary base too.