Your conclusion is good, but your reasoning is not. For instance 8 is a number which is not a perfect square yet has a repeated factor.

A correct way of reasoning this goes as follows:

  1. The number of times the n'th light is pulled is the same as its number of factors.
  2. It will be on if and only if there are an odd number of factors.
  3. If you write out the prime factorization of a number, P1n1 * P2n2 * ... * Pmnm, then the number of factors the number has is (i1 + 1)(i2 + 1)...(im + 1)
  4. This is odd if only if i1, i2, ... , im are all even.
  5. This is true if and only if n is a perfect square.
  6. From 2) and 5), the n'th light is on if and only if n is a perfect square.

In reply to Re^2: CarTalk Puzzler by tilly
in thread CarTalk Puzzler by freddo411

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.