As promised in the previous episode 🙂

Probability to have a duplicate (Y axis) by the number of stickers (X axis) – with an album size of 192 stickers:

The number of distinct stickers (Y axis) by the number of stickers (X axis) – with the album size of 192 stickers:

Made with JPGraph in a few minutes.

The previous post about Panini stickers got into some mathematical formulas. However, the 2 main conclusions were referring to the duplicates probability and distinct probability. That was the mathematical approach to the problem.
Below – the geeky one 🙂

1. Duplicates probability

In a Panini pack of 17 stickers (out of 192 possible stickers), there are 50% chances to have a duplicate.

The geeky way:
– generate a random array of ‘n’ integers in the range [1,192]
– calculate how many duplicates has the array
– repeat this a number of times to get a reliable view.

Results (PHP code at the end of the post):

Number of stickers - Probability of duplicate
10 - 20.47% 
11 - 25.8% 
12 - 31.2% 
13 - 37.13% 
14 - 40.6% 
15 - 45.47% 
16 - 47% 
17 - 53.4%
18 - 58.4% 
19 - 63.27% 
20 - 66.53% 
21 - 69.87% 
22 - 74.53% 
23 - 76.53% 
24 - 80.27% 
25 - 82.33% 
26 - 85.47% 
27 - 86.27% 
28 - 87.87% 
29 - 89.93% 
30 - 91.67% 
31 - 93.73% 
32 - 94.4% 
33 - 94.87% 
34 - 96.07% 
35 - 96.53% 
36 - 97.13% 
37 - 97.47% 
38 - 97.6% 
39 - 98% 
40 - 98.33% 

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The guys behind AlgoRythmics found a brilliant way of showing how the sorting algorithms work: they used popular Romanian and Hungarian dance!
Have a look below how the bubble sort was done:
httpv://www.youtube.com/watch?v=lyZQPjUT5B4
For more dancing watch their YouTube page: they also ‘implemented’ quick sort, insert sort, merge sort and shell sort. You can also play with their sorting tools on their website until you are sure you understood how these sorting algorithms work.
PS – hear and see also the sound of 15 sorting algorithms
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