This Week from Bedtime Math: Wrong Number

How many phone numbers do you think are out there? And how many of them are actually wrong numbers? Try some phone number math to find out!
By Laura Overdeck
May 21, 2013



May 21, 2013

Now that lots of people have cellphones, when they call each other they usually can just tap that person's name from a list, and the phone dials the number already stored in there.  But there was a time when people had to actually dial the right phone number on a "funny-looking" device like the one pictured here.  Even now, when you want to call someone for the very first time, you have to type in the number -- and there's a chance that you will type that number incorrectly.  Given that U.S. phone numbers have 10 digits in them, there's lots of room for error.  In fact, however many right numbers are out there, there are far more wrong ones. Which brings us to this week's Bedtime Math challenge:

Wee ones: (counting on fingers): If your phone number has a 3-digit chunk, then another 3 digits, then another 4 digits, how many digits does your phone number have?

Little kids: If you have a totally cool phone number that ends in -1234, but when people call they dial some wrong digit instead of the 3, how many different wrong numbers could they dial?  Bonus: What if they swap in only odd digits for the 3 -- how many wrong numbers now?

Big kids: If you have the best phone number ever – it's 123-4567 – but when people call you they dial the last three digits in the wrong order, how many different wrong numbers could they dial?  Bonus: What if they mix up all four of the last four digits?  (Tip: you might want to shuffle four objects if that helps you see what's going on.)


Wee ones: 10 digits in total.

Little kids: There are 9 possible wrong numbers, because there are 9 other digits to choose from (0,1,2,4,5,6…)  Bonus: There are now only 4 wrong numbers, because it could be 1, 5, 7, or 9.

Big kids: There are 5 wrong numbers, because there are 6 ways in total to arrange the last three digits: 567, 576, 657, 675, 756, 765 (another way of getting it: 3x2x1).  And the first of those is correct.  Bonus: By the same reasoning, there are 23 wrong combinations, because there are 24 ways to arrange the digits (4x3x2x1).

A message from Laura:   Bedtime Math is a simple idea: we all know we should read to our kids at night, but what about math?   My husband and I have done fun, mischief-loaded math problems with our kids at night for years.  When at age 2, our third child started hollering for his own math problem, we realized we were onto something:  In a world where so many people say "Ewww, math!", we had created a household culture where kids don't just tolerate math, they actually seek it out.   Now we email parents a fun, lively math problem every day to do with their kids – and every week, we'll be posting a new problem right here on Scholastic Parents! 

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