Monday, 25 February 2013

MONDAY, 25 FEBRUARY 2013

Today is the $56^{th}$ day of the year.

$56 = 2^3 \times 7$

$56$ is the number of times that $11$ can be partitioned. A partition of a number is the number of different ways that the number can be written as a sum of integers where the order is not significant. Thus $11$ has the following partitions:

1. $11$
2. $10 + 1$
3. $9 + 2$
4. $8 + 3$
5. $7 + 4$
6. $6 + 5$
7. $9 + 1 + 1$
8. $8 + 2 + 1$
9. $7 + 3 + 1$
10. $7 + 2 + 2$
11. $6 + 4 + 1$
12. $6 + 3 + 2$
13. $5 + 5 + 1$
14. $5 + 4 + 2$
15. $5 + 3 + 3$
16. $4 + 4 + 3$
17. $8 + 1 + 1 + 1$
18. $7 + 2 + 1 + 1$
19. $6 + 3 + 1 + 1$
20. $6 + 2 + 2 + 1$
21. $5 + 4 + 1 + 1$
22. $5 + 3 + 2 + 1$
23. $5 + 2 + 2 + 2$
24. $4 + 4 + 2 + 1$
25. $4 + 3 + 3 + 1$
26. $4 + 3 + 2 + 2$
27. $3 + 3 + 3 + 2$
28. $7 + 1 + 1 + 1 + 1$
29. $6 + 2 + 1 + 1 + 1$
30. $5 + 3 + 1 + 1 + 1$
31. $5 + 2 + 2 + 1 + 1$
32. $4 + 4 + 1 + 1 + 1$
33. $4 + 3 + 2 + 1 + 1$
34. $4 + 2 + 2 + 2 + 1$
35. $3 + 3 + 3 + 1 + 1$
36. $3 + 3 + 2 + 2 + 1$
37. $3 + 2 + 2 + 2 + 2$
38. $6 + 1 + 1 + 1 + 1 + 1$
39. $5 + 2 + 1 + 1 + 1 + 1$
40. $4 + 3 + 1 + 1 + 1 + 1$
41. $4 + 2 + 2 + 1 + 1 + 1$
42. $3 + 3 + 2 + 1 + 1 + 1$
43. $3 + 2 + 2 + 2 + 1 + 1$
44. $2 + 2 + 2 + 2 + 2 + 1$
45. $5 + 1 + 1 + 1 + 1 + 1 + 1$
46. $4 + 2 + 1 + 1 + 1 + 1 + 1$
47. $3 + 3 + 1 + 1 + 1 + 1 + 1$
48. $3 + 2 + 2 + 1 + 1 + 1 + 1$
49. $2 + 2 + 2 + 2 + 1 + 1 + 1$
50. $4 + 1 + 1 + 1 + 1 + 1 + 1 + 1$
51. $3 + 2 + 1 + 1 + 1 + 1 + 1 + 1$
52. $2 + 2 + 2 + 1 + 1 + 1 + 1 + 1$
53. $3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1$
54. $2 + 2 + 1 + 1 + 1 + 1 + 1 + 1 + 1$
55. $2 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1$
56. $1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1$