## November 2022 - Challenge

A sock drawer has b socks of exactly two types: a comfortable socks, and b-a non-comfortable socks. When choosing socks, one picks two socks at random (uniformly) from the drawer.

If a=15 and b=21, the probability of choosing two comfortable socks is exactly \frac{1}{2}. Assuming the sock drawer is magical and can contain a=568345 and b=803761, we also get the probability of \frac{1}{2}.

**Your goal**: find a,b such that the probability for two comfortable socks is exactly \frac{1}{974170}, and such that this is the minimal solution with b having at least 100 digits (minimal with respect to the size of b).

**A bonus** "*" will be given for finding the minimal D such that there are exactly 16 pairs a,b giving the probability \frac{1}{D} with b having less than 100 digits.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

*If you have any problems you think we might enjoy, please send them in. All replies should be sent to:* ponder@il.ibm.com

**Challenge:**
27/10/2022 @ 16:30:00 PM EST

**Solution:**
04/12/2022 @ 12:00 PM EST

**List Updated:**
02/11/2022 @ 12:05 PM EST

#### People who answered correctly:

**Paul Revenant **(30/10/2022 2:40 PM IDT)

**Lazar Ilic **(30/10/2022 3:24 PM IDT)

**Gary M. Gerken **(30/10/2022 5:16 PM IDT)

***Alper Halbutogullari **(31/10/2022 8:47 AM IDT)

***Giorgos Kalogeropoulos **(31/10/2022 12:41 PM IDT)

**Christoph Baumgarten **(31/10/2022 6:52 PM IDT)

***Bertram Felgenhauer **(31/10/2022 11:12 PM IDT)

**Bert Dobbelaere **(1/11/2022 12:29 AM IDT)

***Victor Chang **(1/11/2022 6:38 AM IDT)

**Richard Gosiorovsky**(1/11/2022 12:22 PM IDT)

**Harald Bögeholz **(1/11/2022 3:49 PM IDT)

**Lorenzo Gianferrari Pini **(1/11/2022 6:35 PM IDT)

***Kurt Foster **(2/11/2022 4:38 PM IDT)

***Stéphane Higueret **(2/11/2022 4:39 PM IDT)

**Josh Marza **(2/11/20225:29 PM IDT)

**Dan Dima **(2/11/2022 7:10 PM IDT)

**Davide Colì **(2/11/2022 11:20 PM IDT)

***Prashant Wankhede **(3/11/2022 5:31 AM IDT)

**Michael Liepelt **(3/11/2022 9:21 AM IDT)

**Quentin Higueret **(3/11/2022 2:25 PM IDT)

**Lala Surya **(4/11/2022 4:24 PM IDT)

**Kang Jin Cho **(4/11/2022 7:55 PM IDT)

***Franciraldo Cavalcante **(4/11/2022 8:02 PM IDT)

***Sanandan Swaminathan **(4/11/2022 10:16 PM IDT)

**Aaron Kim **(5/11/2022 4:14 PM IDT)

***Tim Walters **(7/11/2022 1:12 AM IDT)

**A. Ramanujan **(7/11/2022 7:57 AM IDT)

**Wilder Boyden **(7/11/2022 5:55 PM IDT)

***David Greer **(7/11/2022 6:05 PM IDT)

**Mark Beyleveld **(8/11/2022 4:17 PM IDT)

**Laurence Warne **(8/11/2022 6:33 PM IDT)

**Latchezar Christov **(8/11/2022 6:41 PM IDT)