When you look at a digital clock, do you get excited when a cool number show ups? Like a time when all the digits are the same, or when the first two add up to the third? Only a few times each day does the clock do fun tricks like that. On a long car trip, Bedtime Math fans Miriam, Silas, and Titus R. decided to count up how many cool times clocks can show us. They figured out how many times the clock shows all one digit, like 1:11, 2:22…and remembered that those times all show up in the morning, then again in the afternoon. Can you figure out how many times have all the same digit? Let’s find out how many other cool times are worth waiting for — and how often to check the clock to catch them.

*Wee ones:* A clock shows the numbers 1 to 12 on it. Can you name all the numbers between 1 and 12?

*Little kids:* If the time is 5:55, what was the last time before that when all the digits were the same? *Bonus:* Times like 2:35 are cool too, because the numbers can be an equation: here it’s 2+3=5. What equation is happening in the times 7:34 and 2:48?

*Big kids:* How many different times in one day does the clock show all the same digit, like 3:33? *Bonus:* What’s the longest you have to wait between two of those times?

*The sky’s the limit:* What’s the longest you have to wait between times where the first two digits add up to the third — and there’s no 4th digit?

Answers:

*Wee ones:* 2, 3, 4, 5, 6, 7, 8 ,9 ,10, 11.

*Little kids:* 4:44. *Bonus:* We’re subtracting in the first: 7 – 3 = 4. And we’re multiplying in the second: 2 x 4 = 8.

*Big kids:* There are 12 times in one day: 1:11, 2:22, 3:33, 4:44, 5:55, 11:11 in the morning, and then those 6 times repeat in the afternoon. *Bonus:* The gap from 5:55 to 11:11, which is 5 hours 16 minutes (5 hours to get to 10:55, then another 5 minutes to get to 11:00, then another 11 minutes).

*The sky’s the limit:* 3 hours 52 minutes. The earliest time in the day that does this, using the smallest numbers, is 1:01. The latest time is 9:09 since you can’t do 9:90 (only 60 minutes in an hour). Many times work during each of the hours in between, so our biggest wait will be the multi-hour jump from 10:00 through 12:59. So we’re going from 9:09 am to 1:01 pm. That’s 8 minutes less than 4 hours, or 3 hours 52 minutes.

And thank you Miriam, Silas and Titus for sharing this great waiting game!

Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.