## MMM #19: Two winners!

We had 25 submissions for MMM #19 so I decided to give out two prizes! Random.org picked the numbers 6 and 22, which corresponded to the entries from Patrick Swickard and Todd Trimble. Congratulations to the two of you! I'll be contacting you to get you your prizes!

Everyone who submitted an entry got the right answer, which I would expect since a quick calculator check would verify the answer. Some people explained their answers better than others. The most-straightforward solution I saw was this one by Ron Frederick.

This was the problem:

Which is larger, 2.2^{3.3}or 3.3^{2.2}?

Here's Ron's solution:

2.2

^{3.3}= (2.2^{3})^{1.1}

= (2.2 * 2.2 * 2.2)^{1.1}

= (4.84*2.2)^{1.1}

= 10.648^{1.1}3.3

^{2.2}= (3.3^{2})^{1.1}

= (3.3 * 3.3)^{1.1}

= 10.89^{1.1}Since 10.89 is larger than 10.648, 3.3

^{2.2}must be the larger of the two.

Not everyone made the argument that y=x^{1.1} is monotonically increasing when x >= 0 but I didn't hold that against anybody.

There's a new MMM at Blinkdagger right now.

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