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### This Math Problem Is Just Ducky

#### by Julie Leibach

Click to enlarge images
Before beddy-bye, Science Friday guest Laura Overdeck suggests doing some math with your kids. The founder of Bedtime Math, she's making it easy on parents by offering an email option—sign up, and receive a daily math problem suitable for children of various ages. A sample brain teaser follows (and you can listen to Overdeck on SciFri here):

The Problem
It all started in the 1930s, when Frank Schutt, the manager of the Peabody Hotel in Memphis, decided to put three live ducks in the fountain in the hotel lobby for fun. Hotel guests thought it was hysterical, so the owners bumped the number up to five ducks. A few years later, a circus animal trainer trained the ducks to walk on their own up to the fountain every morning and back to their pen at night. To this day, the Peabody Ducks march to and from the fountain every day on a royal red carpet, posing for photos along the way. Hopefully they don't have to carry a suitcase, too.

Wee ones: Apparently the Peabody Hotel fountain had turtles and alligators before the ducks showed up. If the fountain had 8 turtles but now has the 5 ducks, how many more turtles were there than ducks today?

Little kids: The ducks march to the fountain at 11 a.m. every morning and back out at 5 p.m. every afternoon. How many hours do they spend swimming in the fountain each day? Bonus: How many hours each day do they spend outside the fountain? (Reminder: a day has 24 hours.)

Big kids: These probably aren't the same 5 ducks from the 1930s. If all Peabody ducks live 8 years and can be trained when they're 1 year old, what is the earliest year that the current ducks could have started marching? Bonus: If ducks started marching in 1935, what's the least number of sets of ducks the hotel has had to train?

The sky's the limit: The alligators that used to live in the fountain are long gone, fortunately for the ducks. But ducks would be safe with turtles. If we had 7 more ducks than turtles but 18 more turtle feet than duck feet, and the number of duck feet has the same two digits reversed, how many turtles and ducks are walking through the lobby?

Wee ones: 3 more turtles than ducks.

Little kids: 6 hours. Bonus: 18 hours.

Big kids: 2006 (7 years ago). Bonus: That was 77 years ago, so they have to have had 11 sets and are on at least their 12th set.

The sky's the limit: There are 23 ducks and 16 turtles.  If the two foot-count numbers are 18 apart and the digits are reversed, then the two digits themselves are 2 apart: so it's 42, 53, something like that. But they have to be even numbers, so your only choices are 24/42, 46/64, and 68/86. 46/64 gives you animal counts that are 7 apart: 46 duck feet for 23 ducks, and 64 turtle feet for 16 turtles.

Julie is the managing editor of ScienceFriday.com. She is a huge fan of sleep and chocolate. Follow her @julieleibach.

The views expressed are those of the author and are not necessarily those of Science Friday.