Good article!

]]>I have D34 and D50 dipyramid dice in my collection, and I think they have been there before Shapeways existed. My recollection is that they are “lottery dice” (sort of a do-it-yourself quick-pick without a computer), which implies that at one time there existed a state or international lottery that used 34 or 50 numbered balls to choose a winner. So far I have not found such a lottery. I’ve had bad luck getting such info out of Google faster than one state at a time. I don’t intend to buy lottery tickets anyway. You can, of course, use these dice for lottery numbers slightly smaller than these, with a house rule of “re-roll” if you roll a number that is too high. You will also need a house rule for “re-roll if you roll a duplicate number”, as I believe all lotteries disallow a winning number of 5-5-5-5-5-… except maybe the Powerball can duplicate one of the other numbers.

Dice Lab uses a truncated tetrahedron as a d4 and allows for the possibility of landing on an un-numbered small side. Their site gives the probability of that happening as 3% (on a single roll). The chances of rolling 23 times without that happening are less than 50%. (1 – 0.03)^23 = 0.49 Not what I’d call “small”. I think I prefer the dodecahedron with labels, 3 each, of 1, 2, 3, and 4.

You can extend the “Sicherman dice” problem to allow use of dice with any finite number of sides >= 1, for both the problem and the solutions. You tend to get a lot of solutions and I’ve only listed the more interesting ones. “Extended Sicherman” dice giving the same results as 2d4:

1-3-3-5 and 1-2-2-3

1-3 and 1-2-2-3-3-4-4-5

1-2 and 1-2-3-3-4-4-5-6

“Extended Sicherman” dice giving the same results as 2d6:

1-2-2-3-3-4 and 1-3-4-5-6-8 (This is the original Sicherman set, and the only solution using 2 d6’s besides the boring solution of 2 standard-numbered d6’s)

1-2-2-3 and 1-3-3-5-5-5-7-7-9 (Yes, a d4 and a d9. Actually, there are 3 pairs of d4 and d9)

(I omitted typing in the solution involving a d1 and a d36).

“Extended Sicherman” dice giving the same results as 2d8:

1-3-5-5-7-7-9-11 and 1-2-2-3-3-4-4-5

1-3-3-5-5-7-7-9 and 1-2-2-3-5-6-6-7

1-2-5-5-6-6-9-10 and 1-2-3-3-4-4-5-6

Nice reviews of this Campbell trilogy! I just finished these a week ago, and they were fantastic! Maybe it’s me being dense, but since you seem to understand the ending better than I did, perhaps you could explain it. If you’d like to reply directly to my email, so as not to post spoilers, that would be fine.

thanks,

Brian