Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?

Problem K. 517. (November 2016)

K. 517. In Normalia, there is a city in which the people called ,,truetellers'' always tell the truth. Those who are not truetellers will tell the truth one day, and then lie on the following day, then also tell the truth, and so on. The last names of Andrew, Barbara, and Cecilia are Small, Large and Long, in some order. Determine the last name of each of them, given their statements below:

on Monday
Andrew: Barbara is not telling the truth.
Barbara: I am not a trueteller.
Cecilia: There is a trueteller among us.

on Tuesday
Andrew: Cecilia told the truth yesterday.
Barbara: Andrew's last name is either Large or Small.
Cecilia: Barbara's last name is not Small.

(6 pont)

Deadline expired on December 12, 2016.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Barbara nem lehet igazmondó, de most igazat mond, így András nem mond igazat, tehát nem igazmondó. Kedden András már igazat mondott, ezért van igazmondó közöttük. Mivel András és Barbara nem igazmondó, így Cili igazmondó. Barbara hétfőn igazat mondott, így kedden nem, azaz András vezetékneve Hosszú. Cili igazat mond kedden is, így Barbara vezetékneve Nagy. Tehát Cili vezetékneve a megmaradó Kis.


135 students sent a solution.
6 points:94 students.
5 points:7 students.
4 points:10 students.
3 points:14 students.
2 points:1 student.
1 point:3 students.
0 point:6 students.

Problems in Mathematics of KöMaL, November 2016