## Can I Get Your Digits?

*February 23, 2015 at 10:33 pm* *
6 comments *

Saw this on a t-shirt recently:

It made me think about this problem involving digits.

Consider the number

1234567891011121314151617181920obtained by writing the numbers from 1 to 20 in order side-by-side.

What’s the greatest number that can be obtained by crossing out 20 digits?

If a fetching lady or handsome gent catches your fancy by solving that problem, you might want to ask her or him…

How can I know so many digits of π and so few digits of your phone number?

And if he or she still hasn’t taken leave of you, then you could really press your luck with the following:

- Ask your new friend to write down a number with four or more digits.

459,163

- Then, have your friend add the digits.

4 + 5 + 9 + 1 + 6 + 3 = 28

- Subtract the sum from the original number.

459,163 – 28 = 459,135

- Have your friend cross out one of the digits, and then read the remaining number aloud to you.

45,935

- Then, miraculously announce the missing digit.

**1**

The secret to the trick? Simple. Just add the digits of the number that your friend reads aloud, and then figure out what number must be added to get the sum to a multiple of 9. Above, the digits of the number 45,935 have a sum of 26, which is 1 less than a multiple of 9, so the removed digit is 1.

Entry filed under: Uncategorized. Tags: digit, phone, pi, t-shirt, trick.

1.Sam | February 23, 2015 at 11:52 pmAwesome! Would the first one be 91234567892 ?

2.venneblock | March 1, 2015 at 4:36 pmSam, I don’t make it a practice to give away answers. Sara posted a reply that — if correct — would be greater than your answer.

3.Sara | February 24, 2015 at 3:22 pmI can get 95617181920

4.zachdcox | February 28, 2015 at 6:24 pmI posted the steps on my FB page and invited my friends to post their digits and I would ‘magically’ name the missing digit. (And I posted a link to this post with the prefix SPOILER ALERT).

And on G+ I added – ‘Homework – Post A Proof’

5.venneblock | March 1, 2015 at 4:34 pmAwesome! How many people have taken the bait?

6.zachdcox | March 1, 2015 at 8:53 pmSadly, none (so far). But I did write a blog post that explains just how this ‘magic’ works. And I discovered a caveat: If the ‘dropped digit’ is either a 9 or a 0 you can not discriminate between these so you should say in that case: “You left out a ‘0’ or a ‘9’.”

Here is a link to my explanation:

https://zachdcox.wordpress.com/2015/03/01/can-i-get-your-digits-except-for-one-of-them/