October's Challenge

 

A census-taker knocks on a door, and asks the woman inside how many children she has and how old they are.

"I have three daughters, their ages are integers, and the product of the ages is 36," says the mother.

"That's not enough information," responds the census-taker.

"I'd tell you the sum of their ages, but you'd still be stumped."

"I wish you'd tell me something more."

"Okay, my oldest daughter Annie likes dogs."

What are the ages of the three daughters?


Solution by Karla Spence, Holland High School

There are only eight possible combinations of three integers, the product of which equals 36:

Ages
Sum
1
1
36
38
1
2
18
21
1
3
12
16
1
4
9
14
1
6
6
13
2
2
9
13
2
3
6
11
3
3
4
10


Only two of these combinations have identical sums, and both involve twins. Since there is an oldest daughter, the twins must be younger. Thus, Annie is 9, and the twins are 2.

Also solved by: Kara Trisch (Akron-Fairgrove H.S.); Robert Freund, Mark Sipka (Alma H.S.); Charlie Hretz (Bishop Foley Catholic H.S.); Trevor Lambert, Jake Maloney (Catholic Central H.S.); Nick Wimmer (Charlevoix H.S.); Giancarlo Brugnoni, Andrew Jeanguenat, Paul Popiel, Joe Shopp (De La Salle Collegiate H.S.); Joe Meleca, Shawna Wei (Forest Hills Central H.S.); Allison Assaly, Jose Davila, Steve Lambert, Joe Mester, Robert Saliers, Caroline Sierra, Joe Sugiyama, Dani Tyner, Nikkel Westorp, Steven Witte (Forest Hills Eastern H.S.); Grant Boyer, Steve Calhoun, Chris Cooper, Dave Feutz, Evan Klemin, Adam Levick, Kiara Murray, Vishakh Ponnuru, Brian Sebers (Forest Hills Northern H.S.); Alex Bordyukov, Hyunje Cho, Dan Dou, Eva Dou, Alexander Kim, Cathy Krueger (Grosse Pointe South H.S.); Spencer Smith (Holland H.S.); Chelsea Fogwell, David Grund, Nicholas Laban, Susie Skowronek (Lansing Catholic Central H.S.); Rory Aker, Nicholas Donlon, Katae Iordanou, Nicole Konsza, Katie Lamb, Jackie Malmstrom, Alex Perry, Patrick Sage, Cori Snyder, Ryan Stabel, Matt Steibel, Jacqueline Tennis, Jake Thompson, Taylor Thurston, Zac Warner, Matt Weller (Linden H.S.); Scott Pulak, Austin Rose (Marquette H.S.); Shannon Bridges, Mandy Hoffmann, Mary Hogan, Megan Mankevian, Lindsey Reynolds, Claire Wester (Marshall H.S.); Chris Holden, Kat Kuehnert (Novi H.S.); Deanna Abrash, Stephanie Auwers, Matthew Brownell, Karen Cleary, Derek Elenbaas, Armila Francis, Sharon Frank, Brooke Harris, Emily Krause, Aaron Lorincz, Abby Lorion, Patrick Lutz, Sara Ross, Sarah Roth, Matt Saagman, Katie Wendt (Plymouth Christian Academy); Justin Gilliam, Elise Humphries, Kimberly Lebioda, Walter Wang (Plymouth H.S.); Stacy Georges, Cory Jackson (Saginaw Heritage H.S.); Todd Barton, Charles Bunce, Zach Darter, Nate Jerry, Megan Kuehnlein (St. Louis H.S.); Trent Alexander, Dennis Jenks (Vestaburg H.S.); Matthew Beamer (Gettysburg H.S., Gettysburg, PA).