## Friday, 22 February 2013

### THURSDAY, 23 FEBRUARY 2013

Today is the $52^{nd}$ day of the year.

$52 = 2^2 \times 13$

$52$ is the $5^{th}$ Bell Number.

The $n^{th}$ Bell Number is the number of ways you can split up a set containing n elements. The first non-trivial example is when $n = 3$. Assume that we have a set that contains three elements 1, 2 and 3, then the following five partitions are the only distinct divisions of that set:
{1, 2, 3}
{{1} {2, 3}}
{{2} {1, 3}}
{{3} {1, 2}}
{{1} {2} {3}}

$52$ is the $5^{th}$ Bell Number and the $52$ distinct partitions are:
1. {1, 2, 3, 4, 5}
2. {{1}, {2, 3, 4, 5}}
3. {{1}, {2, 3, 4, 5}}
4. {{3}, {1, 2, 4, 5}}
5. {{4}, {1, 2, 3, 5}}
6. {{5}, {1, 2, 3, 4}}
7. {{1, 2} {3, 4, 5}}
8. {{2, 3} {1, 4, 5}}
9. {{3, 4} {1, 2, 5}}
10. {{4, 5} {1, 2, 3}}
11. {{5, 1} {2, 3, 4}}
12. {{1, 3} {2, 4, 5}}
13. {{2, 4} {1, 3, 5}}
14. {{3, 5} {1, 2, 4}}
15. {{4, 1} {2, 3, 5}}
16. {{5, 2} {1, 3, 4}}
17. {{1} {2} {3, 4, 5}}
18. {{1} {3} {2, 4, 5}}
19. {{1} {4} {2, 3, 5}}
20. {{1} {5} {2, 3, 4}}
21. {{2} {3} {1, 4, 5}}
22. {{2} {4} {1, 3, 5}}
23. {{2} {5} {1, 2, 4}}
24. {{3} {4} {1, 2, 5}}
25. {{3} {5} {1, 2, 4}}
26. {{4} {5} {1, 2, 3}}
27. {{1} {2, 3} {4, 5}}
28. {{1} {2, 4} {3, 5}}
29. {{1} {2, 5} {3, 4}}
30. {{2} {1, 3} {4, 5}}
31. {{2} {1, 4} {3, 5}}
32. {{2} {1, 5} {3, 4}}
33. {{3} {1, 2} {4, 5}}
34. {{3} {1, 4} {2, 5}}
35. {{3} {1, 5} {2, 4}}
36. {{4} {1, 2} {3, 5}}
37. {{4} {1, 3} {2, 5}}
38. {{4} {1, 5} {2, 3}}
39. {{5} {1, 2} {3, 4}}
40. {{5} {1, 3} {2, 4}}
41. {{5} {1, 4} {2, 3}}
42. {{1} {2} {3} {4, 5}}
43. {{1} {2} {4} {3, 5}}
44. {{1} {2} {5} {3, 4}}
45. {{1} {3} {4} {2, 5}}
46. {{1} {3} {5} {2, 4}}
47. {{1} {4} {5} {2, 3}}
48. {{2} {3} {4} {1, 5}}
49. {{2} {3} {5} {1, 4}}
50. {{2} {4} {5} {1, 3}}
51. {{3} {4} {5} {1, 2}}
52. {{1} {2} {3} {4} {5}}