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Published online by Cambridge University Press: 19 April 2021
Fix positive integers k and n with
$k \leq n$
. Numbers
$x_0, x_1, x_2, \ldots , x_{n - 1}$
, each equal to
$\pm {1}$
, are cyclically arranged (so that
$x_0$
follows
$x_{n - 1}$
) in that order. The problem is to find the product
$P = x_0x_1 \cdots x_{n - 1}$
of all n numbers by asking the smallest number of questions of the type
$Q_i$
: what is
$x_ix_{i + 1}x_{i + 2} \cdots x_{i+ k -1}$
? (where all the subscripts are read modulo n). This paper studies the problem and some of its generalisations.