PERCOLATION BINGO

1. test box:
 
    0.38   0.67  0.89  0.34

    0.46   0.88  0.45  0.67

    0.78   0.56  0.78  0.34
  
    0.97   0.46  0.74  0.35

try for p=0.5  - if number less than 0.5 mark an X
                 do the X marks connect top to bottom and left to right?
                 connect means above and below or left and right. NOT diagonal!!!!!!
try for p=0.67 - if number less than 0.67 draw another X
                 do the Xs connect??

This was a biased example, the same random numbers for everyone.
(You could make your own box - just write down four rows of four random
numbers from the rand button on your mathematical calculator or smartphone (for iphone use CalcMadeEasy, for android use ...) and test 0.5 and 0.67.)	 

2.  real box:

There are many different computer-generated cases here and more (as well as the generating code)
can be downloaded from
http://phony1.technion.ac.il/~phr76ja/bingo

try for numbers between 0.5 and 0.67 - which is the smallest number where the Xs connect?

    0.5669  0.3137  0.7270  0.8715  0.9423  0.5368  0.7753  0.6772  0.5704  0.7624

    0.3664  0.8185  0.1762  0.0056  0.2849  0.9355  0.8349  0.1230  0.9315  0.7866

    0.9615  0.7080  0.8802  0.6520  0.0211  0.5587  0.6405  0.9830  0.0537  0.6862

    0.9679  0.5123  0.6072  0.3337  0.5676  0.5474  0.1722  0.9725  0.5345  0.6637

    0.7130  0.7471  0.3729  0.5165  0.3873  0.3350  0.9401  0.9921  0.0496  0.6915

    0.1580  0.4139  0.6315  0.6488  0.8355  0.0251  0.9928  0.8363  0.4465  0.4650

    0.3366  0.8924  0.2060  0.4584  0.7831  0.4365  0.2895  0.4367  0.1952  0.7684

    0.5386  0.3090  0.8495  0.7663  0.4962  0.1027  0.0474  0.9497  0.1157  0.6919

    0.2588  0.1777  0.9888  0.3326  0.8928  0.9506  0.4326  0.2229  0.2898  0.7839

    0.2837  0.8076  0.0269  0.6231  0.7403  0.0457  0.1327  0.7683  0.0966  0.3595

3. another real box - try again:

    0.5001  0.5770  0.5588  0.2798  0.0419  0.0404  0.7248  0.6999  0.0007  0.9999

    0.4711  0.4973  0.1179  0.9219  0.3954  0.5560  0.4601  0.0647  0.8655  0.4830

    0.5205  0.3889  0.6652  0.2837  0.1824  0.4925  0.8608  0.1119  0.3872  0.2905

    0.9822  0.0590  0.8522  0.6575  0.1120  0.4541  0.6797  0.7516  0.9768  0.6418

    0.2034  0.2390  0.6343  0.7080  0.9145  0.1379  0.8492  0.1213  0.8117  0.4993

    0.7530  0.7593  0.0185  0.6459  0.8806  0.2880  0.0126  0.1853  0.1771  0.3643

    0.3093  0.5177  0.0700  0.6289  0.9446  0.0565  0.1987  0.9588  0.6006  0.8806

    0.8964  0.9491  0.7170  0.0369  0.0174  0.0913  0.4330  0.2122  0.2046  0.6180

    0.7028  0.9927  0.1892  0.4821  0.4290  0.4302  0.2179  0.4399  0.9568  0.1341

    0.2010  0.7062  0.7739  0.6071  0.6742  0.1505  0.7586  0.0435  0.1695  0.5027