# Dr. Mike’s Big Numbers Contest

For the last day of school, we decided to have all the kids in the school (ages 5-14) spend 5 minutes on Dr. Mike’s “Big Numbers” contest.

The rules, from Dr. Mike were:

- You may write anything at all in the box on the entry form labeled “Write your number here”. I will try to interpret what you write as a number.
- If I cannot interpret what you write as a
**real, finite**number, your entry will be disqualified (in particular,

you can’t write ‘infinity’) - The winner will be the student whose number is bigger than those of all others in the contest
- Your number should fit entirely inside the box, which is 4 inches wide and 2 inches high.

As I mentioned above, we also limited the kids to 5 minutes.

The kids all had a lot of fun, and I think we got a lot more interesting entries than Dr. Mike did. I’ve scanned a few representative and interesting ones here. Please excuse the hard-to-read scans — most of them were written in pencil.

The most popular entry among the 5- and 6-year-olds was:

Slightly older kids (7- to 9-year-olds) tended to come up with entries like these:

This 9-year-old knew about powers (though not their notation) and came up with a really big number….

… though I think not as big as the second of the numbers listed by this eight-year-old (who I think believed that he had written out a googolplex at the top, though in actual fact it is only a googol):

The googol/googolplex theme was popular among the 11-year-olds, though interestingly they all spell it like the search engine😉

The 12-year-olds remembered about factorials!

…and the 13-year-olds combined factorials and powers:

But I’m pretty sure the largest number of all was this entry by the lone 14-year-old in the group (it was his 14th birthday the day of the exercise):

Where do these kids go to school? They know a lot more about numbers than a lot of older kids! Thirteen with factorials is impressive! Powers of powers? WOW!

As I mention in my About page this is a small private school where I volunteer to help teach math a couple of days per week. I do a lot of problem solving and “contest-style” math with the kids. Factorials are fun, and they come up naturally as a result of playing with permutations and combinations types of questions. Powers of powers probably gets mentioned at some point in the overview of order of operations, I’d guess. That’s not something I’ve explicitly done with them. There are several books in the classroom “math library” that deal with big numbers as well, which is probably where they got “googol” from.

I enjoyed this post!

It is fun to see how the kids think!