Coins of Three Different Weights

We discuss several coin-weighing problems in which coins are known to be of three different weights and only a balance scale can be used. We start with the task of sorting coins when the pans of the scale can fit only one coin. We prove that the optimal number of weighings for $n$ coins is $\lceil 3n/2\rceil -2$. When the pans have an unlimited capacity, we can sort the coins in $n+1$ weighings. We also discuss variations of this problem, when there is exactly one coin of the middle weight.Comment: 18 page

On a metamatemEthical question in talent care

Recently more and more ethical issues arise in several sciences. We think that didactics of mathematics is not an exception. In this paper we investigate the question whether we can allow from mathematical precision in talent care. We suggest that these questions origin even from the formulation of a problem. The formulation of three well-known math problem is analized