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March 2019 - Challenge

Every real number can be approximated as a ratio of two integers. For example, pi is close to 22/7 but even closer to 3138/999; and there is an even better approximation with a denominator < 1000 (what is it?).

We define m=BAT(x,N) as the denominator, m, of a fraction k/m which is the best approximation for x with denominator < N.

Let N1 be the number of electrons in one coulomb of electric charge.

Let N2 be energy (measured in electron volts) released in the fusion of 1,000 deuterium atoms and 1,000 tritium atoms to form 1,000 He-4 atoms and 1,000 neutrons.

Find two non-square integers n1 and n2 such that b1=BAT(sqrt(n1),N1)=BAT(sqrt(n2),N1) and b2=BAT(sqrt(n1),N2)=BAT(sqrt(n2),N2) and both b1 and b2 are prime numbers.

Bonus question: for the smallest solution that also satisfy BAT(sqrt(n1),10000)=BAT(sqrt(n2),10000), what is the connection between BAT(sqrt(n1),10000) and IBM? Hint: see April 2011's challenge.

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.

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Challenge: 27/02/2019 @ 12:00 PM EST
Solution: 03/04/2019 @ 12:00 PM EST
List Updated: 03/04/2019 @ 12:00 PM EST

People who answered correctly:

Anders Kaseorg (28/02/19 03:15 AM IDT)
*Harald Bögeholz (03/03/19 01:40 AM IDT)
Todd Will (03/03/19 05:33 PM IDT)
Uoti Urpala (04/03/19 04:48 AM IDT)
*Clive Tong (04/03/19 09:42 PM IDT)
*Dominik Reichl (04/03/19 09:42 PM IDT)
*Eden Saig (05/03/19 12:15 AM IDT)
*Deron Stewart (06/03/19 01:42 AM IDT)
*Daniel Chong Jyh Tar (07/03/19 12:43 AM IDT)
*Michael Rosola (06/03/19 08:53 PM IDT)
*Andreas Stiller (07/03/19 12:36 PM IDT)
Dan Dima (07/03/19 04:39 PM IDT)
*Kang Jin Cho (09/03/19 06:50 PM IDT)
*Deniz Yuret (09/03/19 09:50 PM IDT)
*Haye Chan (10/03/19 02:46 PM IDT)
*JJ Rabeyrin (10/03/19 09:12 PM IDT)
*Alper Halbutogullari (11/03/19 01:58 AM IDT)
*Arthur Vause (11/03/19 07:52 PM IDT)
*Shouky Dan & Tamir Ganor (11/03/19 12:53 PM IDT)
Tom Chen (12/03/19 04:36 AM IDT)
Graham Hemsley (13/03/19 10:41 AM IDT)
Hugo Pfoertner (15/03/19 05:42 PM IDT)
*Reda Kebbaj (16/03/19 10:01 PM IDT)
*Daniel Bitin (17/03/19 06:26 PM IDT)
*David Greer (17/03/19 11:39 PM IDT)
*Adam Daire (19/03/19 07:40 PM IDT)
Thomas Egense (19/03/19 09:48 AM IDT)
Chris Shannon (21/03/19 12:03 AM IDT)
Sanandan Swaminathan (21/03/19 05:26 AM IDT)
*Jeewoo Lee (23/03/2019 04:36 PM IDT)
*Kelvin Kim (23/03/2019 05:33 PM IDT)
*Joonsoo Lee (23/03/2019 06:36 PM IDT)
*Min Jung Kim (24/03/2019 04:59 PM IDT)
Bryce Fore (24/03/2019 08:58 PM IDT)
Vladimir Volevich (25/03/2019 01:12 PM IDT)
*Chuck Carroll (26/03/19 05:53 AM IDT)
*Reda Kebbaj (26/03/19 02:22 PM IDT)
*Marco Bellocchi (26/03/2019 11:54 PM IDT)
*Armin Krauß (28/03/2019 01:08 PM IDT)
*Jiho Lee (30/03/2019 07:51 AM IDT)
Kenneth Kwok (30/03/2019 07:09 PM IDT)
*Dieter Beckerle (30/03/2019 11:58 PM IDT)
*David F.H. Dunkley (31/03/2019 04:42 AM IDT)
*Oscar Volpatti (31/03/2019 09:17 AM IDT)
*Yi Won Kim (31/03/2019 05:46 PM IDT)
Radu-Alexandru Todor (31/03/2019 11:47 PM IDT)
*Vladimir M. Milovanović (01/04/2019 01:49 AM IDT)