  Balance (Counterfeit coin) puzzles have been part of recreational mathematics
for a few decades. A particular type of Counterfeit coin puzzle is known in the
literature as the "Beam balance puzzle". An abstract solution to it is provided
by Iwama et.al as a modification of the Bernstein-Vazirani algorithm, making
use of quantum parallelism and entanglement. Moreover, during this pandemic,
group testing has proved to be an efficient algorithm to save time and cost of
testing specimens for the presence of infection. In this article, we propose a
"Binary Spring Balance" (BSB) puzzle, to facilitate a unified picture of the
counterfeit coin problem and the testing for infection problem, as both aim to
reduce the number of queries. We then showcase two solutions to the BSB
problem, one using bits and other using classical-qubits ('cebits") for
querying. Both solutions are demonstrated using circuits. In this pursuit, we
develop a modified optical implementation of Bernstein-Vazirani algorithm using
only polarizers (no need of beam splitters), which has surprisingly not yet
been proposed earlier. Under the pretext of this demonstration we question why
we have not yet developed testing mechanisms inspired by Bernstein-Vazirani
algorithm for the pandemic, as they solve the problem in single query, they
have no issues related to prevalence of infection in the population, nor are
they plagued by the issue of dilution of samples due to pooling. The modified
implementation of Bernstein-Vazirani algorithm using polarizers can also be a
cost-effective demonstration in an undergraduate lab.

Quantum Physics;Physics Education