Paul the postal carrier had an unusual week involving the ten properties along Park Place. Each day of the week Monday through Saturday he delivered mail to four houses. Eight of the houses received mail on three days and two houses got no mail.

The houses along Park Place are numbered 1 to 10. The sum of the house numbers Paul delivered for each day of the week were:
- Monday: 12
- Tuesday: 18
- Wednesday: 23
- Thursday: 32
- Friday: 25
- Saturday: 19

Which two houses did not receive mail?

(In reply to computer solutions by Daniel)

The 13 ways of getting the same unserved mailboxes:

 1  2  3  6     1  2  3  6     1  2  3  6     1  2  3  6     1  2  3  6
 1  2  5 10     1  2  5 10     1  2  5 10     1  2  5 10     1  2  5 10
 1  5  7 10     1  6  7  9     2  5  7  9     2  5  7  9     3  5  6  9
 6  7  9 10     6  7  9 10     6  7  9 10     6  7  9 10     6  7  9 10
 3  6  7  9     3  5  7 10     3  5  7 10     3  6  7  9     3  5  7 10
 2  3  5  9     2  3  5  9     1  3  6  9     1  3  5 10     1  2  7  9
4  8           4  8           4  8           4  8           4  8

 1  2  3  6     1  2  3  6     1  2  3  6     1  2  3  6     1  2  3  6
 1  2  6  9     1  2  6  9     1  3  5  9     1  3  5  9     1  3  5  9
 1  5  7 10     2  5  7  9     1  5  7 10     2  5  6 10     2  5  7  9
 6  7  9 10     6  7  9 10     6  7  9 10     6  7  9 10     6  7  9 10
 3  5  7 10     3  5  7 10     2  6  7 10     3  5  7 10     2  6  7 10
 2  3  5  9     1  3  5 10     2  3  5  9     1  2  7  9     1  3  5 10
4  8           4  8           4  8           4  8           4  8

 1  2  3  6     1  2  3  6     1  2  3  6
 1  3  5  9     2  3  6  7     2  3  6  7
 2  5  7  9     1  5  7 10     2  5  7  9
 6  7  9 10     6  7  9 10     6  7  9 10
 3  5  7 10     1  5  9 10     1  5  9 10
 1  2  6 10     2  3  5  9     1  3  5 10
4  8           4  8           4  8

 

 

DECLARE SUB deliver (day!)
DIM SHARED noHseUsed, houseCt(10), dayCt(6), hist(6, 4), solCt

CLS

DATA 12,18,23,32,25,19

FOR i = 1 TO 6
 READ dayCt(i)
NEXT

deliver 1

PRINT solCt

END

SUB deliver (day)
 FOR h1 = 1 TO 7
  IF houseCt(h1) < 3 AND (noHseUsed < 8 OR houseCt(h1) > 0) THEN
   houseCt(h1) = houseCt(h1) + 1
   IF houseCt(h1) = 1 THEN noHseUsed = noHseUsed + 1
   FOR h2 = h1 + 1 TO 8
     IF houseCt(h2) < 3 AND (noHseUsed < 8 OR houseCt(h2) > 0) THEN
      houseCt(h2) = houseCt(h2) + 1
      IF houseCt(h2) = 1 THEN noHseUsed = noHseUsed + 1
   FOR h3 = h2 + 1 TO 9
     IF houseCt(h3) < 3 AND (noHseUsed < 8 OR houseCt(h3) > 0) THEN
      houseCt(h3) = houseCt(h3) + 1
      IF houseCt(h3) = 1 THEN noHseUsed = noHseUsed + 1
     
            h4 = dayCt(day) - h1 - h2 - h3
            IF h4 > h3 AND h4 <= 10 THEN
              IF houseCt(h4) < 3 AND (noHseUsed < 8 OR houseCt(h4) > 0) THEN
               houseCt(h4) = houseCt(h4) + 1
               IF houseCt(h4) = 1 THEN noHseUsed = noHseUsed + 1
              
               hist(day, 1) = h1
               hist(day, 2) = h2
               hist(day, 3) = h3
               hist(day, 4) = h4
                         
              
               IF day = 6 THEN
                r0 = (solCt \ 5) * 10 + 1
                c0 = (solCt MOD 5) * 15 + 1
                FOR i = 1 TO 6
                 FOR j = 1 TO 4
                  LOCATE r0 + i, c0 + (j - 1) * 3
                  PRINT USING " ##"; hist(i, j);
                 NEXT
                 PRINT
                NEXT
                solCt = solCt + 1
              
                LOCATE r0 + i, c0
                FOR i = 1 TO 10
                  IF houseCt(i) = 0 THEN PRINT i;
                NEXT
                PRINT : PRINT : PRINT
               ELSE
                 deliver day + 1
               END IF
           
               houseCt(h4) = houseCt(h4) - 1
               IF houseCt(h4) = 0 THEN noHseUsed = noHseUsed - 1
              END IF
            END IF
     
      houseCt(h3) = houseCt(h3) - 1
      IF houseCt(h3) = 0 THEN noHseUsed = noHseUsed - 1
     END IF
   NEXT h3
      houseCt(h2) = houseCt(h2) - 1
      IF houseCt(h2) = 0 THEN noHseUsed = noHseUsed - 1
     END IF
   NEXT h2
   houseCt(h1) = houseCt(h1) - 1
   IF houseCt(h1) = 0 THEN noHseUsed = noHseUsed - 1
  END IF
 NEXT h1
 
END SUB

 

Posted by Charlie on 2009-11-17 14:32:59