Category Archives: Math

Bracket Math

I love March Madness! Not only is it a chance for me to watch 4 basketball games at one time, I get to geek out with some ridiculously large numbers—the odds of producing a perfect bracket prior to the tournament. For this exercise, we will limit ourselves to the round of 64 and beyond (since the NCAA can’t trick us into pretending we care about the First Four unless our team is playing).

Basic Probability

Number of teams- 64

Number of games- 63

This is way more obvious than most people realize so you can stop counting the blanks on your bracket. If one team is eliminated in every game, it will take exactly 63 eliminations (games) to leave one team victorious.

Possible outcomes of each game- 2

One team will win, one team will lose.

Possible number of brackets- 2^63 = 9,223,372,036,854,775,808 (over nine quintillion)

If you don’t understand basic probability, here is a crash course. Multiply the number of possible outcomes of an event times the number of possible outcomes of every other event. In this case…

2 (the number of possible outcomes of the first game) x 2 (the number of possible outcomes of the second game) x 2 (the number of possible outcomes of the third game)…x 2 (the number of possible outcomes of the 63rd game) = 2^63 power.

If you don’t trust that math, work it out with a simple 4 team bracket:

four team bracket possibilities

There are only four possible winners of the tournament, but there are two different ways for each team to win because there are two possible opponents for each winner in the championship game. To verify the math…

2 (the number of possible outcomes of the first game) x 2 (the number of possible outcomes of the second game) x 2 (the number of possible outcomes of the third game) = 8

2^3=8

Astronomical Numbers

Understanding 9,223,372,036,854,775,808 possible brackets

If you printed out 1,000 brackets you would have a stack of paper 8 inches tall.

Print 1,000 brackets 999 more times you would have one million brackets.

You now have enough 8 inch stacks to cover ¼ of a basketball court.

Repeat that whole process 999 more times and you will have one billion (1,000,000,000) brackets that are now covering 250 basketball courts in 4 inches of paper.

You would need to repeat this entire process over 9 billion (9,000,000,000) more times in order to have every possible bracket.

If you printed that many brackets…

  • You would be able to cover over 76.5 billion basketball courts up to the height of the rim.
  • You would be able to make 6,261 stacks of paper that reached the sun. and still have one-tenth of a stack left over.
  • If you enlisted the help of every person on earth (all 7,000,000,000 of us) to make one unique bracket per minute with no breaks to sleep, eat, or do anything else…we would finish a few months after the tournament ended in the year 4519.
  • From the time the bracket is finalized to the time entries are locked in most contests is about 89 hours. In order to have all of the brackets printed in time, you would need to have a computer capable of printing 28,787,054 brackets every nanosecond.

But don’t bother with all of that…

I made out the perfect bracket this year and have already spent Warren Buffet’s $1,000,000,000.

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Easy as Pi

Have you ever noticed how ridiculously specific the Bible is when describing the structures that were built in the worship of God? Cubits, acacia wood, pitched within and without, cherubim, ox blood… There’s a lot of detail. Which is why this verse describing the molten sea in Solomon’s temple is surprising:

Then he made the sea of cast metal. It was round, ten cubits from brim to brim, and five cubits high, and a line of thirty cubits measured its circumference. -1 Kings 7:23 (ESV)

That pool’s dimensions are given again in 2 Chronicles:

Then he made the sea of cast metal. It was round, ten cubits from brim to brim, and five cubits high, and a line of thirty cubits measured its circumference. -2 Chronicles 2:4 (ESV)

The surprising part is that the math doesn’t work out. Mathematicians have used the Greek letter pi to represent the ratio of a circle’s circumference to its diameter. Simply put: π = circumference / diameter.

The Bible clearly states that this pool was circular, that its diameter was 10 cubits, and its circumference was 30 cubits. Here’s the math:

That just doesn’t make sense. Every seventh grader can tell you that pi is approximately 3.14. Most seventh graders can tell you that the circumference of this pool should have been 31.4 cubits. So is the Bible wrong?

Some, while trying to defend the Bible’s creditability, have stated that the figures are merely estimates. This seems very unlikely considering the detail in the descriptions surrounding these two passages. Some have speculated that the pool was not completely circular but elliptical. This is problematic because the passages only give one measurement across. An oval shape would have been wider one direction than the other. I would have expected both measurements to have been given.

I believe the solution is much, much simpler. A few verses later, we are given a little more of a physical description of the pool.

Its thickness was a handbreadth, and its brim was made like the brim of a cup, like the flower of a lily. It held two thousand baths. -1 Kings 7:26 (ESV)

This handbreadth-wide brim may be the missing piece to the formula. It is possible that the two measurements were measuring two different circles. One circle (ten cubits from brim to brim) at the edge of the pool and the other (thirty cubits measured its circumference) at the edge of the water.

So, in order to do the math, I converted the units to inches using my own arm and hand. I’m going with an even 18 inches per cubit and 4 inches per handbreadth.

Once we subtract four inches from each side of the circle, we have an inner circle with a diameter of 14.33 feet and a Biblically stated circumference of 45 feet.

That looks about right to me.

Conjunctions and Confusion and Criticism

Read this number out loud:

7,312

Don’t worry about the strange looks other people in the room will give you. Just do it.

7,312

Did you read “seven thousand, three hundred and twelve”?

Well, you’re wrong. The number actually reads “seven thousand, three hundred twelve.” The word and should not be used after the hundreds place but only to designate a fractional part of a number. For some reason it drives me nuts to hear “six hundred and thirty-five” or “a hundred and three.”

You like using the word and in numbers? Here’s your chance: 3.4 should be read “3 and four tenths.” Use and to separate the whole number from the fractional part. No, I’m not saying “three point four” is wrong, I’m just using the word and correctly in a mathematical context. Please don’t get me started on hyphens (here are the mathematical rules for that if you’re curious).

I probably shouldn’t get so bent out of shape about this, but this morning the and rule had an impact on my life. You see, I’m about 40 chapters behind in my B90X Bible reading so I have come up with a great way to stay motivated and, hopefully, still finish the entire Bible by September 13:

  • Skip ahead to where I should be. For some reason it is very discouraging for me to read what I should have read a few days ago so I just skipped those 40 chapters and joined up where I should have been had I not been slacking.
  • Listen to the parts I missed. I am using the YouVersion app on my iPad and the time I spend doing things I really don’t have to think about (showering, shaving, getting dressed, etc.) to listen to the passages I missed. I have really enjoyed listening to about six chapters a day.

The plan was working flawlessly until this morning when I was listening to Ezra 2. The guy with the really cool accent who was reading to me kept throwing the and into the numbers. Not all of the numbers, mind you, but he was blatantly butchering the English language on about fifty percent of them. As I was shaving, this was all I could think about. My mind went from critiquing Max McClean’s recording to my own six-year-old daughter’s misuse of the conjunction to her school teachers’ obvious failures to my need to correct the world on proper mathematical grammar to outlining this blog post. Before I knew it I was shaved, dressed, and putting on my shoes…that’s when I heard Mr. McClean say “Ezra chapter five.”

I missed two and two thirds chapters of the book of Ezra because I was nitpicking a guy’s reading! I have no clue what happened in those chapters. I have no idea what God wanted me to glean from that passage of scripture. I completely missed it! So maybe I shouldn’t be worried about changing the way the English-speaking world says three-digit numbers. Maybe I should worry about not letting my critical mind get between me and God’s Word.

After I hit pause (I didn’t want to make the same mistake again), I thought about how I’ve done the same thing with preachers and teachers. How many times have I critiqued their grammar, speaking styles, word choice, or illustrations to the point that I completely missed what God had for me that day? How much more could I learn if I start listening to the real Teacher rather than the way the messenger presents His truth? All of this was racing through my mind while I tied my shoes and paid no attention to what my hands were doing. After all, they’ve done it thousands of times. I don’t want to listen to God’s messages for me the same way I tie my shoes.