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):

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