LEGO block distributions
Recently, after purchasing a couple of 'purple buckets' of basic LEGO building blocks, I took the time to count the distribution of pieces before throwing them in with my myriad other bricks. The label on the outside of the bucket stated that there were 400 bricks inside... would that be true? would each bucket contain exactly 400 bricks? and would each contain the same number of each type of brick (color and size)?
Fortyfive minutes and two empty purple buckets later I had my answers:
LEGO set #2494 ('Purple Bucket') 

1x1 
1x2 
1x3 
1x4 
1x6 
1x8 
2x2 
2x3 
2x4 
2x6 
Color Total 
white 
20 
20 
8 
14 
8 
2 
10 
4 
8 
1 
95 
blue 
20 
20 
8 
14 
8 
2 
10 
4 
8 
1 
95 
red 
17 
16 
6 
12 
6 
4 
8 
4 
7 
1 
81 
yellow 
17 
16 
6 
12 
6 
4 
8 
4 
7 
1 
81 
black 
12 
10 
4 
8 
2 
2 
4 
2 
4 
0 
48 
Size Total 
86 
82 
32 
60 
30 
14 
40 
18 
34 
4 
400 TOTAL 
As you can see, yes, there were, in fact, exactly 400 bricks in each bucket... and each bucket contained exactly the same number of each piece. Whew  I can sleep at night. Some interesting notes:
 There are equal numbers of white and blue bricks as well as red and yellow bricks.
 The black bricks seem to get a raw deal: by far the fewest number when partitioned by color (keep that in mind when you set out to build a LEGO Darth Vader).
 The small 1x1's are the most common by size.
 Each brick has a number of 'pips' equal to its width times height; the total number of 'pips' in the bucket is: 1466.
And now for 'the big blue tub'...
LEGO set #3033 ('Blue Tub') 

1x1 
1x2 
1x3 
1x4 
1x6 
1x8 
2x2 
2x3 
2x4 
2x6 
Color Total 
white 
40 
60 
12 
40 
8 
4 
40 
12 
24 
4 
244 
blue 
40 
60 
12 
40 
8 
4 
40 
12 
24 
4 
244 
red 
40 
60 
12 
40 
8 
4 
40 
12 
24 
4 
244 
yellow 
40 
60 
12 
40 
8 
4 
40 
12 
24 
4 
244 
black 
20 
28 
8 
24 
0 
0 
20 
8 
12 
0 
120 
green 
12 
28 
4 
20 
0 
0 
20 
8 
12 
0 
104 
Size Total 
192 
296 
60 
204 
32 
16 
200 
64 
120 
16 
1200 TOTAL 
Notes:
 This is obviously not just three times the number of bricks in the 400pc Purple Bucket above (there are green bricks for one thing).
 #3033 contains no green or black 1x6 or 1x8's (!)
 In fact, those lengths are rather few in number for all colors.
 White, blue, red and yellow have the same numbers of each size brick.
 The 'Silver Anniversary' tub (LEGO #3026) had this same brick count + 1 Silver 2x4.
 I also have a webpage that details how the pieces are grouped within the buckets when first opened.