All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Renumbered Dice (Posted on 2004-07-20)
Two standard dice are renumbered so that each die is different, but together the pair still gives the same probabilities for rolling sums of 2 to 12 as a standard pair.

If each die is numbered with integers all greater than 0, then what are the numbers on the renumbered dice?

 Submitted by Brian Smith Rating: 3.1667 (6 votes) Solution: (Hide) The alternate dice are numbered [1 2 2 3 3 4] and [1 3 4 5 6 8] The probability distrbution for standard dice can be generated by powers of the polynomial d(x)=(x+x^2+x^3+x^4+x^5+x^6). The coefficient of x^k gives the frequency out of 6^n. For two dice: (x+x^2+x^3+x^4+x^5+x^6)^2 = x^2+2x^3+3x^4+4x^5+5x^6+6x^7+5x^8+4x^9+3x^10+2x^11+x^12 An alternate factorization of the polynomial is (x+x^3+x^4+x^5+x^6+x^8)*(x+2x^2+2x^3+x^4) The first factor represents a die with faces [1 3 4 5 6 8]. The other factor represents a die with faces [1 2 2 3 3 4]. Gamer found a site with a similar solution here.

Comments: ( You must be logged in to post comments.)
 Subject Author Date These dice are commercially available :-) Percy 2005-11-16 17:05:18 got it with computer vectorboy 2004-07-26 16:24:24 Solving way Gamer 2004-07-20 15:33:53 ummm... Thalamus 2004-07-20 12:06:25 Problem Edit Brian Smith 2004-07-20 11:39:52 add/subtract Ady TZIDON 2004-07-20 08:46:28

 Search: Search body:
Forums (0)