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Graphical Solutions to Instant Insanity Puzzles, Combinatorics of These Puzzles, and Their Generalizations
1.4 Instant Insanity
So far, our motivation for studying graph theory has largely been one of philosophy and language. Before we get too much deeper, however, it may be useful to present a nontrivial and perhaps unexpected application of graph theory; an example where graph theory helps us to do something that would be difficult or impossible to do without it.
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MAS 341: Graph Theory
Lecture 2: Instant Insanity, Isomorphisms
"Instant Insanity" is the name given by Parker Brothers to their 1967 version of a puzzle which has existed since antiquity, and which has been marketed many toy and puzzle makers under a variety of names, including: "Devil's Dice" (Pressman); "DamBlocks" (Schaper); "Logi-Qubes" (Schaeffer); "Logi Cubes" (ThinkinGames); "Daffy Dots" (Reiss); "Those Blocks" (Austin); "PsykoNosis" (A to Z Ideas), and many others.
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Instant Insanity Puzzle | Infinite Series
About the Oracle of Bacon
This is the most comprehensive version of the Kevin Bacon game on the web. The object of the game is to start with any actor or actress who has been in a movie and connect them to Kevin Bacon in the smallest number of links possible. Two people are linked if they've been in a movie together. We do not consider links through television shows, made-for-tv movies, writers, producers, directors, etc. For example, you might wonder how Mary Pickford can be connected to Kevin Bacon. One answer is that:
Mary Pickford was in Coquette (1929) with Louise Beavers was in All the Fine Young Cannibals (1960) with Robert Wagner (I) was in Wild Things (1998) with Kevin Bacon
Then we can count how many links were necessary and assign the actor or actress a Bacon number. Bacon numbers higher than 4 are very rare. In the example above, Mary Pickford has a Bacon number of 3. The Oracle uses the data from the Internet Movie Database and can give you the shortest path from every actor and actress that can be connected to Kevin Bacon.
(E?)(L1) http://www.wolframalpha.com/examples/PlottingAndGraphics.html
Extended Keyboard - Directly enter math and other symbols.
Plotting & Graphics
Functions
plot a function of one variablespecify an explicit range for the variable
- plot x^3 - 6x^2 + 4x + 12
- graph sin t + cos (sqrt(3)t)
- plot 4/(9*x^(1/4))
plot a function where it is real-valued
- plot e^x from x=0 to 10
plot a special function
- real plot -(sqrt(25-y^2))
plot several functions
- plot Ai(x)
plot a function on a logarithmic scale
- plot sin x, cos x, tan x
- plot x e^-x, x^2 e^-x, x=0 to 8
plot on a log-linear scale
- log plot e^x-x
3D Plots
- log-linear plot x^2 log x, x=1 to 10
plot a function of two variablesspecify explicit ranges for the variables
- plot sin x cos y
Equations
- plot x^2 y^3, x=-1..1, y=0..3
plot the solution to an equation in two variablesInequalities
- plot 3x^2-2xy+y^2=1
plot the region satisfying an inequality in two variablesplot a region satisfying multiple inequalities
- plot |x|^3+|y|^3<1
Polar Plots
- plot x^2+y^2<1 and y>x
draw a polar plotspecify a range for the variable theta
- polar plot r=1+cos theta
Parametric Plots
- polar plot r=theta, theta=0 to 8 pi
draw a parametric plotspecify a range for the parameter
- parametric plot (cos^3 t, sin^3 t)
Number Lines »
- parametric plot (sin 10t, sin 8t), t=0..2pi
visualize a set of real numbers on a number lineshow multiple sets on a number line
- number line 2, 3, 5, 7, 11, 13
- number line x^2>5, 0<=x<3
