Do you ever ever ask in math class, “When are we ever going to need to use this?” or in Jewish studies classes, “Yeah, but how does this apply to me?” Well, in this column, I answer both questions at the same time! Math and Judaism have a lot in common and both can be taught better if they incorporate each other.

This Week’s Question

Did you know that just a few days ago many congregations started to blow the shofar after morning services? Although the yearly mitzvah of hearing the shofar only applies to Rosh Hashanah, there is a long-standing custom to sound it during the month of Elul (that is the month before Rosh Hashanah) every morning. The idea is that hearing the shofar will wake us up spiritually and encourage us to better ourselves before the days of Rosh Hashanah and Yom Kippur.

There is an important exception to this practice: We do not sound the shofar on the last day of Elul since we need to distinguish between the custom during these days of Elul and the actual mitzvah of hearing the shofar on Rosh Hashanah. Since Elul has 29 days, this means there are 28 days of blowing the shofar during the month of Elul.

Here’s a related math problem:

Shlomo and Rivky both have birthdays during the month of Elul but they have funny ways of telling people which days they are. That is, they talk about their birthdays by describing how many days of shofar blowing there are in the month before their birthday and how many after.

Shlomo said, “If you take the number of days of blowing the shofar before my birthday, divide it by two and add six, then you get the number of days left of blowing the shofar after my birthday.”

Rivky said, “If you take the number of days left of blowing the shofar after my birthday, multiply it by two and subtract three, then you get the number of days of blowing shofar before my birthday.”

Whose birthday comes earlier in the month of Elul and by how many days?

Solution

This problem can be solved quickly using algebra, but in case you don’t know that yet there is another way of solving it (If you are interested in the algebra approach the two equations to start with are at the bottom of this non-algebra solution.)

To solve this problem without algebra, first make a table with 28 rows (one for each day of the month that the shofar is blown) with three columns for each row. The columns should be the day of the month, then how many days of shofar blowing are before, and then how many days of shofar blowing are after. Here is an example with the first three and last three rows filled in.

It might take you some time to find the right answers but eventually you can determine that Shlomo’s birthday is 15 Elul and Rivky’s birthday is 18 Elul. This means that Shlomo’s birthday is three days earlier than Rivky’s.

This checks because in the case of Shlomo’s birthday, there are 14 days of shofar blowing before and half of this is 7. When you add 6 to 7 you get 13, which is the number of shofar blowing days after 15 Elul. For Rivky, there are 10 days of shofar blowing after her birthday. Twice of this is 20 and when you subtract 3 you get 17, which is the number of shofar blowing days before 18 Elul.

Using algebra we can let S be the variable for Shlomo’s birthday and R be the variable for Rivky’s birthday. Then the two equations are:

(S – 1)/2 + 6 = 28 – S

R – 1 = 2(28 – R) – 3

I hope you have a wonderful month of Elul as we prepare for Rosh Hashanah!

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