Seven - The Solutions
July 21, 2008

There are 6(6) = 36 possible rolls.

Of these, only the following pairs total 7.

1, 6

6, 1

2, 5

5, 2

3, 4

4, 3

Thus the probability of Brent rolling a sum of 7 is 6/36 or 1/6.

Lets make a diagram.

If Grumpy gets his way there are only two orders that he, Bashful and Sleepy can sit in; Bashful, Grumpy, Sleepy or Sleepy, Grumpy, Bashful.

For the four remaining seats there are 4 dwarfs left to sit in them; thus, there are 4(3)(2)(1) = 24 orders that the other four dwarfs could sit in.

This means that in total there are 2(24) = 48 distinct orders that the seven dwarfs could sit in.

900/7 = 128.6 degrees, to the nearest tenth

Carol number:

n = 1               4¹ − 2^{(1 + 1)} − 1 = 4 – 4 – 1 = –1

n = 2                4² − 2^{(2 + 1)} − 1 = 16 – 8 – 1 = 7

n = 3                4³ − 2^{(3 + 1)} − 1 = 64 – 16 – 1 = 47

Kynea number:

n = 1                4¹ + 2^{1 + 1} − 1 = 4 + 4 – 1 = 7

n = 2                4² + 2^{2 + 1} − 1 = 16 + 8 – 1 = 23

Finally, 47 − 23 = 24