Sunday, March 30, 2014

I Do Not Feel So Bad About My Bracket Picks

The One Billion Dollar Prize Pay Out Was A Safe Bet

Last night Evelyn and I watched FL "whup up on" DAYTON but did not stay up late enough to see Wisconsin upset Arizona.  

Today it could work out that University of Michigan and Michigan State University both make it into the final four.  

I heard yesterday that the 1 BILLION DOLLAR contest to make a perfect NCAA bracket pick is now officially over, absolutely no one who entered a bracket has it all right so far.  

Which is not surprising since the odds against a completely perfect bracket are 1:18,446,744,073,709,551,616 against or in english:

The odds against picking a perfect are:

one to 
eighteen quintillion
four hundred forty six quadrillion 
seven hundred forty four trillion 
seventy three billion 
seven hundred nine million 
five hundred fifty one thousand 
six hundred sixteen 

These are pretty small odds and the folks that put up one billion dollars against this event occurring were pretty sure their money was safe.  

Even after eliminating all the possible ways that four number 16 seeds could wind up in the final four are eliminated their money is safe.  

And even just accounting for the fact that the last eight teams were all ranked their money was safe.

And most importantly even accounting for all the different ways two number one seeds, two number two seeds, a seven seed, an eight seed, and an eleven seed could make to the final eight (which is what actually happened) then their money was safe.  

This is because the number different of ways at 1,1,2,2,7,8,11 seed can arrive in the final eight is so large the money is safe.

The final 8 brackets were: (1,11) (4,7) (1,2) and (8,2)

Great8  Final4  Final2  Champ  Final2 Final4   Great8
1 ------+ (1)                          (2)  +------ 1
        +------+        -----        +------+
11 -----+      |          |          |      +------ 2
               +--------- v ---------+
4 ------+      |                     |      +------ 8
        +------+                     +------+
7 ------+                                   +------ 2

So there is just ONE way that the above 'Great-8' bracket could be but to GET-THERE there are lots and lots of ways.  Just considering the #1 Seed in the upper left hand corner (University Of Florida) it was only ONE of SIXTEEN teams that could have been there.  So assuming it made it then in the previous round there were EIGHT DIFFERENT OPPONENTS it could have had.  And in the previous round there were FOUR and in the previous TWO so that is 8*4*2 or 64 different ways it could arrive at where it was. This is true for all eight teams so there are 64*64*64*64*64*64*64*64 = 64^8 = 281,474,976,710,656 which in english is: 

two hundred eighty-one trillion 
four hundred seventy-four billion 
nine hundred seventy-six million 
seven hundred ten thousand 
six hundred fifty-sixth

So even though lots and lots of people picked (Florida vs Dayton AND Michigan St vs UCON AND Arizona vs Wisconsin AND Kentucky vs Michigan) NO BODY PICKED exactly HOW they got where they got. since the actual path those eight teams was one way out of 281,474,976,710,656 different ways.

Saturday, March 22, 2014

Third Bike Ride of the Year

A Nice Spin Down "The Neuse River Trail"

The weather is supposed to go down-hill tonight through the middle of next week so this afternoon was a good chance for a ride.

I parked near the Falls of the Neuse Dam and rode the trail all the way to Anderson Point Park and back.

The whole trail is about 50 kilometers long so this ride covered more than half the whole thing.

The statistics were 55 kilometers in about 2.5 hours, averaging over 20 kilometers per hour.

Saturday, March 15, 2014

Second Bike Ride of the Year

A Very Nice Spin on the Greenway

This day I rode my new bike.  There is a saying, "It is not about the bike."  This is correct.  However, my new bike does throw into very sharp relief just how crappy the engine is.

hh:mm:ss .... 01:38:31
kilometers .. 31.45
kph average . 19.50
kph maximum . 59.20 --- Woah!(37mph - definitely downhill)

The ride today did not have a lot of climbs, as compared with the one last Sunday.  I rode down Yadkin to Crabtree Creek and turned left onto Alleghany and rode on up past the CCC-Golf-Course and down the hill to the corner of White Oak and Lassiter Mill.  Turned left and crossed Crabtree Creek and got on the greenway. I followed the greenway all the way to Crabtree Blvd. and Raleigh Blvd.  When you cross over Raleigh Blvd. you find the greenway is closed for construction.  There were two bikes just in front of me that kept going but I turned around and rode the greenway all the way back to Lassiter Mill where I rode up Lassiter Mill drive up to White Oak and turned right and rode back to Yadkin where I rejoined the greenway and rode to the other end at Lindsey Dr.  I took a break and ate part of my banana and swapped the water bottles around and rode back to Yadkin and then back up the hill to home.

Wednesday, March 12, 2014

How Many Numbers Do You Speak

How Many Numbers Do You Speak When Counting Backwards?
Can Someone Speak For
(dd:hh:mm:ss) is: 03:16:45:00 (correction: see below)

Note:  The motivation for this post can be found at the following link: "".  Of course I do not know how many videos will be eventually posted but I can imagine that there will be 999 videos with this same topic. This post was written the same day 9:91 was posted.

Suppose you were to speak the numbers backwards from 99 down to 1, how many numbers would you speak?  The answer seems pretty easy: The following set when spoken aloud yields ninety-nine numbers: {99, 98, 97, ..., 10 , 9, 8, 7, 6, 5, 4, 3, 2, 1}.

Now suppose you are looking at a microwave oven timer and you enter 1:99.  This is taken by the microwave software as the input one minute and ninety-nine seconds.  This gives the following set of numbers: {199, 198, 197, ..., 110, 109, 108, 107, 106, 105, 104, 013, 102, 101, 100, 59, 58, 57, 56, ..., 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}.

Notice when the count reaches 100 it then continues with 59, 58, 57, down to 1. so entering 199 in a microwave only yields 99+60 or 159 numbers. In a similar manner entering 299 yields 99+60+60 or 219 numbers.  

Now suppose you enter 9:99 how many numbers do you get?

And finally suppose you enter 9:99 and count backwards. Next, at the end you enter 9:98 and count backward, then at the end you enter 9:97 and so forth all the way to 0:99, 0:98, 0:97, ...,  0:05, 0:04, 0:03, 0:02, 0:01.  

What is the total?

The Answer:

Below is a python app that, I think, computes the number of numbers.  The grand total is very large.

The Answer
The Better Answer:
A much shorter way to say all the numbers is to understand that once you have spoken a number you no longer need to speak it again you can just refer to the one already spoken.  This is in the best tradition of Mathematics.  Once something is done then it stays done!

The total number of spoken numbers remains the same but we can organize them for reuse.

For example:  the set {0:99, 0:98, 0:97, ..., 0:03, 0:02, 0:01 } contains the set {0:98, 0:97, ..., 0:03, 0:02, 0:01} and so forth all the way down to the set {0:03, 0:02, 0:01) and finally the set {0:01}.

When we apply this to speaking the numbers displayed on the microwave we get the following kinds of sets.

The 39 Second Sets:  These are the numbers from, for example: 

9:99 down to 9:60, or 
8:99 down to 8:60, and 
so on down to 
0:99 down to 0:60.  

There are 10 of these sets. And we see they take up 390 seconds total.

The 60 Second Sets:  These are the numbers from, for example:
9:59 down to 9:00, or 
8:59 down to 8:00, and 
so on down to 
1:59 down to 1:00 and finally 
0:59 down to 0:01.  

There are 10 of these sets and they take up 590 seconds total.

Adding these numbers together we get 989 seconds or 16 minutes and 29 seconds.

Sunday, March 09, 2014

First Bike Ride Of The Year 2014

A Very Nice 1:30 H:MM  25.5 KM Bike Ride

My first bike ride of the year.  After I got my new bike last September I felt bad about the old bike, it had served me so well over the years since 1999.  So I tried to find some replacement shifters (105-Triple-9Speed) on EBay and I did.  Last week I had them installed and the bike tuned up and I took it out for my first ride of the year 2014.  

Here is a "Google-Earth-KML-File" of the ride.  Also here is a link to my "Map-My-Ride-Page" and the bike ride is named "A Very Nice Greenway Ride".

The ride started at the house then went down Yadkin Drive to Crabtree Creek where I got on the greenway and rode all the way upstream to the end of the greenway.  Then it was back the way I came till I arrived back at Crabtree Valley Mall.  Next I headed along Blue Ride Road to the House Creek Greenway Trail and rode that all the way up to the pedestrian/bike overpass at the intersection of I440 and Wade Avenue.  Once across I440 on the bridge it was down hill and up hill to the North Carolina Museum of Art.  I took the bike trail 'around-back' and hooked up with Blue Ridge Road again and rode that back down the hill toward Crabtree Creek and getting off on old Edwards Mill Road and on down the hill to the greenway where I retraced my route back home.