BedtimeMathFoundation.org | Contact Us

A Backwards Day

by Laura Overdeck

A palindrome is a word that is spelled the same backwards and forwards, like toot and racecar. Can you think of any others? It turns out numberscan do the same thing — like today’s date! Today is written as 9/19/19, which means the 19th day of the 9th month (September). In fact, we’re just ending a whole stretch of palindrome days, starting with 9/10/19 up to today. Don’t forget, 9/1/19 was a palindrome, too! We’ve been having cool streaks like this for the past few years, like 8/13/18, and 7/12/17…see if can you figure out when they happen, and when they don’t!

Wee ones: How do you say “123” in backwards order?

Little kids: If you say “221” in backwards order, is it the same or different? How about 454?   Bonus: How old will you be the next time your age is the same backwards and forwards?

Big kids: If you add up all the digits in today’s date (9 + 1 + 9 + 1 + 9), how much greater is the sum than the sum of the digits of this month’s first palindrome, 9/1/19?  Bonus: The digits of 9/1/19 add up to 20. What’s the next date that will add up to 20 this way?

The sky’s the limit: If you’re allowed to write both the month and year as 2 digits, when’s the first year when we won’t have any palindromic dates? (For example, in 2020 you can write February as 02).

 

 

 

 

 

 

 

 

 

 

 

Answers:

Wee ones: 321.

Little kids: 221 then reads 122, so it’s not a palindrome. But 454 does work!  Bonus: Different for everyone…any single digit works, like 7, 8 or 9! Or your next age might be 11, or 22…or 101!

Big kids: It’s 9 more. You can actually figure this out without doing any addition – there is one more 9 in today’s date, and all the other digits are the same! Bonus: 10/9/19 is the next date with digits that add up to 20. You know it can’t be a September date, because 9/x/19 gives you a sum of 19. October dates give you a sum of 11 between the month and year (10/x/19 = 1 + 0 + 1 + 9 = 11). If 11 + x = 20, then x must equal 9.

The sky’s the limit: We’ll have the same kinds of dates in 2019 (/10/19, 9/11/19…), and in 2020 we can have them in February (02/1/20 through 02/9/20, plus 02/11/20). We’ll also have a couple in 2021 (for example: 1/2/21, 1/21/21, and 12/1/21 through 12/9/21, as well as 12/11/21 and 12/22/21). Then in 2022 we’ll have 2/2/22, 2/20/22, 2/21/22 and so on. That’s true throughout the ’20s, with dates like 3/20/23, all the way through 9/29/29. In 2030 we start over with 03/1/30, then 1/3/31. This pattern will continue through the ’40s, ’50s, all the way to 9/9/99 in 2099. 2100 is the first year we won’t have one, because we can’t have 0/0/00!

Top