Each of the five students - Andy, Danny, Ellen, Janice and Sammy received different marks in a mathematics quiz which was held last week. Students who made correct statements had obtained higher scores than those who made incorrect statements.

The following are the statements made by the five students:

Sammy: Andy and Ellen gained the top two places.
Janice: No, what Sammy just said is incorrect.
Danny: I was ranked in between Sammy and Janice.
Andy: Janice came second.
Janice: I had obtained a lower score than Ellen.
Ellen: Exactly three of the previous five statements are correct.

Determine the order in which the five students finished.

CLS
FOR a = 1 TO 5
 used(a) = 1
FOR d = 1 TO 5
 IF used(d) = 0 THEN
  used(d) = 2
FOR e = 1 TO 5
 IF used(e) = 0 THEN
  used(e) = 3
FOR j = 1 TO 5
 IF used(j) = 0 THEN
  used(j) = 4

  s = 15 - a - d - e - j
  used(s) = 5

  strue = (a < 3 AND e < 3)
  j1true = NOT strue
  dtrue = (d < s AND d > j OR d > s AND d < j)
  atrue = (j = 2)
  j2true = (j > e)
  ptruect = ABS(strue + j1true + dtrue + atrue + j2true)
  etrue = (ptruect = 3)
  t(a) = ABS(atrue)
  t(d) = ABS(dtrue)
  t(e) = ABS(etrue)
  t(j) = ABS(j1true)
  t(s) = ABS(strue)
  good = 1
  FOR i = 1 TO 4
    IF t(i) = 0 AND t(i + 1) = 1 THEN good = 0
  NEXT
  t(j) = ABS(j2true)
  FOR i = 1 TO 4
    IF t(i) = 0 AND t(i + 1) = 1 THEN good = 0
  NEXT
' IF j1true <> j2true THEN good = 0
  IF good THEN
    FOR i = 1 TO 5
     IF used(i) = 4 AND j1true <> j2true THEN
       PRINT "j x    ";
     ELSE
       PRINT MID$("adejs", used(i), 1); t(i); "   ";
     END IF
    NEXT
    IF j1true = j2true THEN PRINT "*";
    PRINT
  END IF

  used(s) = 0

  used(j) = 0
 END IF
NEXT
  used(e) = 0
 END IF
NEXT
  used(d) = 0
 END IF
NEXT
 used(a) = 0
NEXT

lists some possibilities, with the starred one being the expected answer, in which Janice did not alternate truth with falsehood:

a 1    j x    s 0    d 0    e 0
a 1    j x    e 0    s 0    d 0
a 1    j x    s 0    e 0    d 0
j x    a 0    s 0    d 0    e 0
j x    a 0    e 0    s 0    d 0
j x    a 0    s 0    e 0    d 0
j x    s 0    a 0    d 0    e 0
e 1    j 1    a 1    s 0    d 0    *
j x    e 0    a 0    s 0    d 0
j x    s 0    a 0    e 0    d 0
j x    s 0    d 0    a 0    e 0
j x    e 0    s 0    a 0    d 0
j x    s 0    e 0    a 0    d 0
j x    s 0    d 0    e 0    a 0
j x    e 0    s 0    d 0    a 0
j x    s 0    e 0    d 0    a 0

where the scores are listed from highest to lowest, and a 1 next to the name indicating truth and a zero falsehood.

In the non-starred cases, Janice told one lie and one truth, indicated by an x. In a sense it could be said in these cases that "students who made correct statements had obtained higher scores than those who made incorrect statements", especially the first three cases, where a strict truth teller finished ahead of Janice.

Posted by Charlie on 2014-02-10 12:57:57