Jim Propp’s self-referential aptitude test is quite interesting. It’s a difficult puzzle but here are some hints/spoilers:
- Q1 states that Q1-5 must have at least one B.
- Q3 states that the number of Qs with answer E is 0-4.
- Q4 states that the number of Qs with answer A is 4-8.
- Q6 Answer to Q17 is C, D or E.
- Q8 states that the number of Qs with answer of A is 4-8.
- Q9 states that Q10 is A or Q11 is B or Q12 is C or Q13 is D or Q14 is E.
- Q11 states that there are 0-4 Qs before it with answer B.
- Q13 states that either 9,11,13,15,17 are A.
- Q14 states that the number of Qs with answer D are 6-10.
- Q17 states that the answer to Q6 is C, D, or E.
I’m sure everyone has seen this joke:
“There are 10 types of people in the world. Those who understand binary and those who don’t.”
I prefer the following version that goes as follows:
There are 10 kinds of people in the world:
- those who understand trinary,
- those who don’t understand trinary
- and those who mistake it for binary.
A team of researchers has shown that no position of the Rubik’s cube requires more than 20 moves by using around 35 CPU-years of idle computer time donated by Google. The algorithms used by those fast cube solvers typically require more than 40 moves.
“One may suppose God would use a much more efficient algorithm, one that always uses the shortest sequence of moves; this is known as God’s Algorithm. The number of moves this algorithm would take in the worst case is called God’s Number. At long last, God’s Number has been shown to be 20.”
It should be noted that there exists configurations of the Rubik’s cube which require at least 20 moves to solve, as shown by Michael Reid who proved that the ”superflip” position requires 20 moves.
(by “The Cyberiad” by Stanislaw Lem)
Come, let us hasten to a higher plane,
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n,
Commingled in an endless Markov chain!
Come, every frustum longs to be a cone,
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.
In Riemann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.
I’ll grant thee random access to my heart,
Thou’lt tell me all the constants of thy love;
And so we two shall all love’s lemmas prove,
And in our bound partition never part.
For what did Cauchy know, or Christoffel,
Or Fourier, or any Boole or Euler,
Wielding their compasses, their pens and rulers,
Of thy supernal sinusoidal spell?
Cancel me not–for what then shall remain?
Abscissas, some mantissas, modules, modes,
A root or two, a torus and a node:
The inverse of my verse, a null domain.
Eclipse of bliss, converge, O lips divine!
The product of our scalars is defined!
Cyberiad draws nigh, and the skew mind
Cuts capers like a happy haversine.
I see the eigenvalue in thy eye,
I hear the tender tensor in thy sigh.
Bernoulli would have been content to die,
Had he but known such a2 cos 2ϕ!
A math professor has a problem with his plumbing, so he hires a
plumber. He watches the plumber use a wrench to tighten a joint, then
is handed a bill for a couple hundred dollars. “I had no idea that
plumbers made this much money!” he said, “I’ve been a math professor
for 20 years and I can’t claim to make this much per hour.”
So the professor decides to become a plumber and for a while he’s very
happy. Then the licensing board decides that plumbers need to know more
math, and the professor, along with all the other plumbers, have to
attend a math class. The teacher called on him one day to go to the
board and compute the circumference of a circle. The professor gets to
the board, but for some reason, he can’t remember the formula to
determine the circumference. So he decides to derive the formula.
The professor fills the board with calculations, but at the end he gets
a formula that he knows is incorrect. Figuring he made a mistake
somewhere along the line, he erases all his calculations and starts
again, but again he gets the same incorrect answer. He’s stumped! He
stares at the blackboard and tries to figure out what he’s doing wrong.
Then, in unison, all the other plumbers say, “Switch the limits on your integral!”