3

Part of 1999 Czech and Slovak Match

Problems(1)

exactly k pairwise non-congruent triangles of sides

Source: Czech and Slovak Match 1999 P3

Find all natural numbers

k

for which there exists a set

M

of ten real numbers such that there are exactly

k

pairwise non-congruent triangles whose side lengths are three (not necessarily distinct) elements of

M

.

real numbercongruent trianglescombinatorics