Ucitel si mysli dve prirozena cisla vetsi nez 1. Dva studenti maji za ukol uhodnout ktera. Prvnimu studentovi povi soucin techto cisel a druhemu soucet.
Prvni: "Neznam soucet."
Druhy: "To jsem vedel. Soucet je mensi nez 14."
Prvni: "To jsem vedel. Ale ted uz cisla znam."
Druhy: "Ja take."
Jaka byla ta cisla?
Oznacte cisla pismeny A, B. Cache je ukryta ve vzdalenosti 3*A*B-A metru v azimutu (A-B)*(A+B) od pocatecnich souradnic (azimut i vzdalenost jsou prirozena cisla).
The teacher has two natural numbers in mind, both greater than 1. Two students are supposed to guess them. The first student is told their product, the other student hears their sum.
First: "I don't know the sum."
Second: "I knew that. The sum is smaller than 14."
First: "I knew that. But now I know the numbers."
Second: "So do I."
What were the numbers?
Call the numbers A, B. The cache is hidden 3*A*B-A metres in azimuth (A-B)*(A+B) from the original coords (both the distance and azimuth are natural numbers).