# Some Silly Math Problem

A friend caused me to stay up rather late a few nights ago by posing the following math problem:

Ein Student stellt seinen zwei Mathematikprofessoren eine Aufgabe. Er überlegt sich zwei Zahlen zwischen 1 und 50 und sagt dem einen Professor die Summe und dem anderen das Produkt und verpflichtet sie, die Zahlen nicht auszutauschen.

Nach einigem Überlegen ruft der Professor mit der Summe den mit dem Produkt an und sagt ihm: "Du kannst nicht draufkommen." Kurz danach ruft der mit dem Produkt den mit der Summe an und meint: "Jetzt weiß ich's!" Wieder kurze Zeit später ruft der mit der Summe den mit dem Produkt zurück und meint: "Jetzt hab' ich's auch!"

Welches waren die beiden Zahlen?

Auf Englisch:

A student give his two math professors a problem. He thinks of two numbers between 1 and 50 and tells the one professor the sum of the two and the other professor the product of the two. He tells them they can't tell each other their numbers.

After some thought, the professor who knows the sum calls the professor who knows the product and tells him "you can't figure it out." Shortly afterwards the professor who knows the product calls the professor who knows the sum "Now I know the two numbers!" After another short while, the professor who knows the sum calls the professor who knows the product back and says "Now I know them too!"

What were the two numbers?

Step through my thought process by clicking along the pages at the top. The most relevant pages are bold. The page labelled answer is just the answer. Only click there if you just want the two numbers and any other text is too much for you.

I have learned to be very suspicious of ideas I cannot express well in both Dutch and English: as nice as it is to have the union at one's disposal, it is wise to confine oneself to the intersection.
-- Edsger Wybe Dijkstra