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May 2023 - Challenge
This problem was suggested by Lorenzo Gianferrari Pini and Radu-Alexandru Todor - thanks!
Let be a length
vector
and
be an
matrix. We seek to compute the quadratic form
.
Assume is equally spaced between
and
, e.g., for
, we have
The matrix is generated in the following manner:
Let be a natural number and define a vector
that is equally spaced between
and
, i.e.,
for
. The values of
will be taken from the vector
in the following manner:
We are given a sequence , with each
being a vector of
natural numbers. Given two such vectors, define
as the binary vector of length
that has 1s in the entries that are equal in
and 0s in the other entries. Let
be the natural number whose binary representation is
, where the least significant bit is on index 0. For example, if
=
(since the vector
stands for the binary representation 1010).
Now define .
So one can think of as taking on a value from a fixed list of
values based on the "similarity" between
and
.
The values of the 's are chosen pseudo-randomly using the formula
For example, if , then
A bonus "*" will be given for finding
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:
01/05/2023 @ 15:30 PM EST
Solution:
05/06/2023 @ 12:00 PM EST
List Updated:
20/06/2023 @ 14:35 PM EST
People who answered correctly:
*Lazar Ilic(1/5/2023 4:26 PM IDT)
Lorenz Reichel(1/5/2023 6:25 PM IDT)
*Yan-Wu He(1/5/2023 10:24 PM IDT)
Amos Guler(2/5/2023 12:25 PM IDT)
*Alper Halbutogullari(2/5/2023 10:59 PM IDT)
*Bertram Felgenhauer(3/5/2023 1:49 PM IDT)
Dieter Beckerle(4/5/2023 5:52 PM IDT)
Sanandan Swaminathan(4/5/2023 5:55 PM IDT)
Julien Pradier(5/5/2023 5:27 PM IDT)
*Martin Thorne(5/5/2023 7:40 PM IDT)
Gary M. Gerken(6/5/2023 4:56 PM IDT)
*Li Li(7/5/2023 1:53 AM IDT)
Evan Semet(7/5/2023 3:26 AM IDT)
Philip Bui(7/5/2023 4:04 AM IDT)
*Harald Bögeholz(7/5/2023 8:05 AM IDT)
*Lawrence Au(7/5/2023 5:02 PM IDT)
Asaf Zimmerman(7/5/2023 6:14 PM IDT)
Lorenzo Gianferrari Pini(8/5/2023 12:29 PM IDT)
*Guy Daniel Hadas(8/5/2023 9:41 PM IDT)
*Peter Moser(9/5/2023 8:41 PM IDT)
Sachal Mahajan(10/5/2023 2:15 AM IDT)
Joram Meron(10/5/2023 12:58 PM IDT)
Stéphane Higueret(12/5/2023 7:21 AM IDT)
Daniel Chong Jyh Tar(12/5/2023 9:30 PM IDT)
Victor Chang(13/5/2023 5:04 AM IDT)
Michael Liepelt(13/5/2023 8:16 AM IDT)
*Dominik Reichl(13/5/2023 7:53 PM IDT)
*David F.H. Dunkley(14/5/2023 2:44 AM IDT)
*David Greer(14/5/2023 9:00 PM IDT)
Marco Bellocchi(16/5/2023 11:14 AM IDT)
*Daniel Chong Jyh Tar(16/5/2023 1:14 PM IDT)
*Tim Walters(16/5/2023 10:29 PM IDT)
*Andreas Stiller(17/5/2023 3:25 PM IDT)
Daniel Bitin(17/5/2023 6:50 PM IDT)
*Vladimir Volevich(18/5/2023 10:57 AM IDT)
*Dan Dima(18/5/2023 3:30 PM IDT)
Reda Kebbaj(19/5/2023 6:11 PM IDT)
*Bert Dobbelaere(19/5/2023 9:38 PM IDT)
*Daniel Copeland(21/5/2023 4:17 PM IDT)
*Daniel Mayer(21/5/2023 11:01 PM IDT)
Phil Proudman(22/5/2023 7:25 PM IDT)
*Hok Leung Nip(23/5/2023 8:10 PM IDT)
*Motty Porat(27/5/2023 3:21 AM IDT)
*Reiner Martin(27/5/2023 6:14 PM IDT)
Shouky Dan & Tamir Ganor(29/5/2023 11:56 AM IDT)
Latchezar Christov(30/5/2023 1:23 PM IDT)
*Diane Pham(31/5/2023 12:07 PM IDT)
*Kang Jin Cho(31/5/2023 7:51 PM IDT)
*Balakrishnan V(1/6/2023 5:48 AM IDT)
Nyles Heise(1/6/2023 7:56 PM IDT)
Matt Cristina(2/6/2023 12:55 AM IDT)
*Vaskor Basak(2/6/2023 2:52 PM IDT)