For the HPCC readers, Wlodek presented the riddle in DATAFILE V18N5P13.
For the PCX readers, a (faulty) Dutch translation of the riddle was published in
PCX Info V5N3P1, so we had to correct for it in PCX Info V5N4P2…

The silences of Mrs. Hypatia

Once, Mrs. Hypatia was asked how old each of her two daughters was.
The question was asked by three very strong mathematicians.

She replied:
“My daughters are different in age and each older than 12 months and younger than 21 years…” (So all whole numbers from 1 to 20 are possible solutions!)

The three mathematicians exclaimed together: “With this information we can’t find the solution yet !”

“The sum of the squares is…” and she whispered the first mathematician a number into the ear.

“The difference of the squares is…” and she whispered the second mathematician a number into the ear.

After this, Mrs. Hypatia kept silence for a while…

The three mathematicians exclaimed together:
“With this information we can’t find the solution yet !”

And again, Mrs. Hypatia kept silence for a while…

And again, the three mathematicians exclaimed together:
“With this information we can’t find the solution yet !”

But hardly had they said this, when all three, also the one who had not been told any number, exclaimed together:
“Eureka ! Now we do know the solution !”

And you ? Do you also know the solution now ?