10Nov/088

## MMM #19: Which is larger?

Troy Williams was announced as the winner for MMM #18 over at Blinkdagger. Congratulations, Troy!

Now it's time for MMM #19.

I have a Rubik’s Revolution, courtesy of Techno Source (or $10 Amazon.com gift certificate, if you prefer, or $10 in USD via PayPal to non-US folks) to give to the winner.

Here's the problem:

Which is larger, 2.2^{3.3}or 3.3^{2.2}?Show how to solve this problem without use of a calculator, or log table, or slide rule.

You should be able to solve it with just paper and pencil.

Here are the rules for the contest:

- Email your answers with solutions to mondaymathmadness at gmail dot com.
- Only one entry per person.
- Each person may only win one prize per 12 month period. But, do submit your solutions even if you are not eligible.
- Your answer must be explained. You must show your work! Wild About Math! and Blinkdagger will be the final judges on whether an answer was properly explained or not.
- The deadline to submit answers is Tuesday, November 18, 12:01AM, Pacific Time. (That’s Tuesday morning, not Tuesday night.) Do a Google search for “time California” to know what the current Pacific Time is.)
- The winner will be chosen randomly from all timely well-explained and correct submissions, using a random number generator.
- The winner will be announced Friday, November 21, 2008.
- The winner (or winners) will receive a Rubik’s Revolution or a $10 gift certificate to Amazon.com or $10 USD via PayPal. For those of you who don’t want a prize I’ll donate $10 to your favorite charity.
- Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.
- I may post names and website/blog links for people submitting timely correct well-explained solutions. I’m more likely to post your name if your solution is unique.

notedscholarNovember 10th, 2008 - 17:49

I hope I can win!

AnneleenNovember 12th, 2008 - 02:21

I guess that the points in this problem are used to represent decimal places?

(In Europe (or is it just Belgium?) we tend to use a , for decimals, and a point usually represents multiplication.)

MgcclNovember 12th, 2008 - 08:40

@Anneleen

Why must Europe do things differently? I feel comma for decimal point very awkward.(I mean… it’s called a decimal “point” not decimal “comma”)

MikeNovember 13th, 2008 - 04:53

It doesn’t matter what Europe or any other society use for their currency notation. This is mathematics.

In math, a lower dot is used to separate integral parts of a number and its fractional parts, a center dot is used for scalar multiplication, and commas are used to distinguish between multiple conditions.

OguzNovember 14th, 2008 - 10:49

At first, I only read the last part of Anneleen’s comment, ((In Europe (or is it just Belgium?) we tend to use a , for decimals, and a point usually represents multiplication)) I thought this comment was unnecessary. Then I realised 2.2 means 2/10 and Anneleen was trying to say that:)

To Mgccl; Europe doesn’t do things differently. Actually US does. Because maths has developed in Europe and Asia mostly thanks to French, Italian and Arabic. We use comma like they do, for decimal “point”. But the thing is, “point” is just some verbal mistake probably done by Americans, because we use “decimal comma” in Turkish as it is supposed to be. Point represents multiplication as Anneleen said.

ThisIsMathematics!!!!!November 19th, 2008 - 09:59

Contrary to Mike’s assertion, “Mathematics” doesn’t specify the decimal separator to be a dot. Yes, a decimal point is common in English-speaking countries. True, pocket calculators tend to feature a decimal point. But a decimal comma (yes, Mgccl, it’s called a decimal comma) is used in most of Europe and South America. For non-currency related math. And I hear they do a fair bit of math in Europe.

My question, now that the contest is over: which is larger, 90 or 88?

huyNovember 19th, 2008 - 17:47

hey, does anyone know what happened to blinkdagger?

SolNovember 19th, 2008 - 18:11

Huy — Blinkdagger is having an issue with their ISP.