Here’s another math problem to prepare for Chanukah. One day during Chanukah, Sarah overheard two of her friends talking:

Rivky said, “My family lit a total of 15 candles last night!” Leah said, “Well, my family beat yours. We lit a total of 21 candles!”

Before she overheard them, Sarah wasn’t sure what day of Chanukah it was and how large Rivky’s and Leah’s families were. Now she knew all of that. What did she know now and how could she figure it all out?

Solution: Sarah knew that the previous night was the third night of Chanukah, that there are five people in Rivky’s family and seven in Leah’s family. Here’s how:

When people light candles during Chanukah, they light the number of candles for that night of Chanukah. That means that in a home where everyone lights, the total number of candles lit equals the night of Chanukah times the number of people in the home. Let’s look at the possibilities for Rivky’s and Leah’s families.

For Rivky’s home with 15 candles it could be:

Night 1 x 15 people

Night 3 x 5 people

Night 5 x 3 people

For Leah’s home with 21 candles it could be:

Night 1 x 21 people

Night 3 x 7 people

Night 7 x 3 people

The only possibilities for a night in common are Night 1 and Night 3. If it was the first night of Chanukah, that would mean Rivky has 15 people in her home and Leah has 21 people in her home. This is a possibility but we usually don’t see homes with 21 people. Instead, Night 3 is more logical. If we look at the lists, this means that Rivky has five people in her family and Leah has seven people. Shabbat Shalom.

Ari Blinder is a math educator living in Highland Park and the owner of Math for the Masses, an innovative math tutoring and consulting company. For more information, visit www.math4masses.com. Ari can be reached at [email protected].