# 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:

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.

## 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.