Finally, A Post

Remember, past performance is not an indication of future results.

Explanation: This may be the golden rule of being the parent of a newborn child. Not only do we not have a schedule in our house, but every time I think we have a schedule, it changes on me. Let's hope the same holds true for the stock market, huh?

In Case You Care: The answer to last week's math problem is (x-1)(y-1) - 1. So, for x=5 and y=11, the biggest number that cannot be made out of 5's and 11's is 4*10-1 = 39. Sure enough, if you consider the numbers that can be made from 5's and 11's, the list looks like this:

0 = 5*0 + 11*0
5 = 5*1 + 11*0
10 = 5*2 + 11*0
11 = 5*0 + 11*1
15 = 5*3 + 11*0
16 = 5*1 + 11*1
20 = 5*4 + 11*0
21 = 5*2 + 11*1
22 = 5*0 + 11*2
25 = 5*5 + 11*0
26 = 5*3 + 11*1
27 = 5*1 + 11*2
30 = 5*6 + 11*0
31 = 5*4 + 11*1
32 = 5*2 + 11*2
33 = 5*0 + 11*3
35 = 5*7 + 11*0
36 = 5*5 + 11*1
37 = 5*3 + 11*2
38 = 5*1 + 11*3
40 = 5*8 + 11*0
41 = 5*6 + 11*1
42 = 5*4 + 11*2
43 = 5*2 + 11*3
44 = 5*0 + 11*4

At this point, we have reached a string of five consecutive numbers (our x), which means we can make all numbers greater than that by simply adding multiples of 5 to 40, 41, 42, 43, or 44.

As I can't remember enough number theory to write a proof here, I'll leave that as an exercise for the reader.

Sorry for the missing post yesterday and the late one today - it has been a busy week for me.