carlo@oscvax.UUCP (Carlo Sgro) (09/06/84)
Here at the Science Centre, we've been working on a computerized version of the
card game 'Concentration'. Our version uses the operations of addition,
subtraction, multiplication, and division. A target is given and
the cards revealed must add, subtract, multiply, or divide to that target.
However, as you've probably deduced already, to have a large number of
distinct pairs requires a very large target in the case of multiplication.
Hence, we've abandoned the plans as being too impractical. However, it
inspired intellectual curiosity here as to how to find the Greatest Lower
Bound. To me, the problem seems to be thus:
Let the target product be t.
Let d1, d2, d3, ..., dn divide t with corresponding mates m1, m2, m3,
..., mn (i.e. mi * ni = t).
t and di's are positive integers. All di's are distinct.
Find the lowest t for any given integer n.
It seems to me that A solution is t = LCM(d1,d2,...,dn,m1,m2,...,mn) but this
would not be the GLB. Any solutions??