Oregonians for Rationality booth
The Cantankerous Cube
five by five by five
|You probably start
solving this puzzle by filling the lowest layer with blocks. When
you have just one more piece to add to the layer—assuming that you haven't yet used any
of the little "stick" pieces (1X1X3)—you will discover that a stick piece
is the only kind of piece that can fill up the layer.
From this point on
you can guarantee frustration, failure and fultility in a very simple way:
just put two of those sticks so that they lie in the same plane,
Any plane. There are fifteen planes in the finished 5X5X5 cube.
Five are horizontal, like the one illustrated below at the bottom of the
puzzle. And five stand up vertically running front to back and another
five stand up vertically running left to right.
Puzzle pieces by John Denoma.
The problem is that all the other pieces add an even number of little 1X1X1 units, and every plane has 25 of those units, an odd number. Only the sticks can add an odd number. Each stick will add an odd number to five different planes: it will add one unit in three different planes and three units to two planes. So there's just enough stick pieces to go around with none to spare. Put two into any one plane, and you won't have enough to go around.
go a little further.
Statistics is seldom understood very well. In fact, statistics is most often seen as a pack of lies told us by people who think like advertisers and political campaign managers. Pick and choose your stats and you can "prove" any damn thing you wish. Wishsful thinking with a PR twist! . . . PAP!
The scientific truth lies in a completely different dimension: statistics is one of the most powerful tools in the scientist's toolbox. And any scientist who picks and chooses his or her data to prove a point will soon be doing something else for a living...perhaps PR for a politician? (This isn't a precaution for just the would-be scientist: everybody should become able to handle a little statistical reasoning. It is, for example, important in economics: in the stock market, the state lotteries, the gambling casinos, in ordering manufacturing materials...everywhere.)
We might consider the odds of getting that pesky 5X5X5 cube together. If you don't know about distributing those stick pieces with perfect frugality, what are the odds of your putting two of them into one plane. Almost a certainty, of course. Your odds of success, then are about the same as your odds of winning the big one in a state lottery: "ZERO, to eight significant figures."
Bob Park's phrase. See What's NewAt Da Vinci Days, O4R demonstrated something that, several years ago, became an embarrassment to a lot of professional mathematicians who demonstrated that they didn't understand the logic. It's a puzzle that Marylin vos Savant once put in her Parade column. Monty Hall once used it, too.
The puzzle experiment was run using random placement of the prize—randomness is one of the statistical concepts that needs better public understanding The results of two days of people answering that puzzle were tabulated with hazel nuts in clear-walled columns. Seeing the running tabulation gave a clear answer to the problem, even if you couldn't work it out logically for yourself.
Look at the results. Do you think some other kind of nuts would have helped people see the "obvious"?
.................................107 48 94 170
It's clear that those who chose "Switch" were far more likely to win than those who chose "Stay."
And those who played had a strong bias toward "Stay" (that is, LOSE).
(May 24, 2003: go to "Probability")
Da Vinci Days, 2002