A Professor asked four students how long each of them had been studying.

One of the students replied: “We have all been studying a whole number of years, the sum of our years of studying is equal to the number of years you have been teaching and the product of our years of studying is 180”.

“I’m sorry”, replied the Professor after some thought, “but that doesn’t give me enough information”.

“Yes, you’re right”, agrees another of the students. “But if we told you that one of us were into double figures in our years of study, then you could surely answer your question”.

How long had each of the four been studying ?

(In reply to solution by Charlie)

The list of ways to factor 180 into 4 factors was produced from sorting the output of the following program by total:
DECLARE SUB factorit (n!, lev!)
DIM SHARED fact(4)
n = 180
OPEN "factors.txt" FOR OUTPUT AS #1
factorit n, 1
CLOSE
END

SUB factorit (n, lev)
  IF lev = 1 THEN strt = 1: ELSE strt = fact(lev - 1)
  IF lev = 4 THEN
    IF strt <= n AND n >= fact(lev - 1) THEN
      strt = n:
    ELSE
      EXIT SUB
    END IF
  END IF
  FOR i = strt TO n
    IF n \ i = n / i THEN
      fact(lev) = i
      IF lev = 4 THEN
       tot = 0
       FOR j = 1 TO 4
        PRINT #1, USING "###"; fact(j);
        IF j < 4 THEN PRINT #1, "+"; : ELSE PRINT #1, "=";
        tot = tot + fact(j)
       NEXT
       PRINT #1, tot
      ELSE
       factorit n / i, lev + 1
      END IF
    END IF
  NEXT
END SUB

Posted by Charlie on 2003-04-28 03:59:00