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Multiple Choice Test (Posted on 2003-06-07) Difficulty: 4 of 5
Select the correct answer to each question.

1. The correct answer to Question 2 is
A. B
B. C
C. D
D. A

2. The correct answer to Question 4 is
A. D
B. C
C. A
D. B

3. The first question for which C is the correct answer is
A. 4
B. 2
C. 3
D. 1

4. The number of questions for which B is the correct answer is
A. 1
B. 2
C. 3
D. 4

5. The number of even-numbered questions for which either B or C is the correct answer is
A. 1
B. 3
C. 0
D. 2

6. The last question for which A is the correct answer is
A. 6
B. 7
C. 5
D. 8

7. The number of instances where D is the correct answer for two consecutive questions is
A. 2
B. 0
C. 1
D. 3

8. The only letter which is the correct answer to exactly three questions is
A. C
B. D
C. B
D. A

See The Solution Submitted by Bryan    
Rating: 4.4091 (22 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Brute force method. | Comment 2 of 19 |
For this problem the brute force method is the only way I know.

The following program goes through all the possibilities (the only simplifying logic being that the possible answer to 1 determines questions 2 and 4 as well). A through D are represented by 1 through 4 respectively.

CLS
FOR q1 = 1 TO 4
  q2 = q1 MOD 4 + 1
  SELECT CASE q2
   CASE 1
    q4 = 4
   CASE 2
    q4 = 3
   CASE 3
    q4 = 1
   CASE 4
    q4 = 2
  END SELECT
  FOR q3 = 1 TO 4
    FOR q5 = 1 TO 4
      FOR q6 = 1 TO 4
        FOR q7 = 1 TO 4
         FOR q8 = 1 TO 4
           q(1) = q1
           q(2) = q2
           q(3) = q3
           q(4) = q4
           q(5) = q5
           q(6) = q6
           q(7) = q7
           q(8) = q8
           'eval q3
           leastC = 0
           FOR i = 1 TO 8
             IF q(i) = 3 THEN leastC = i: EXIT FOR
           NEXT
           IF q3 = 1 AND leastC = 4 OR q3 = 2 AND leastC = 2 OR q3 = 3 AND leastC = 3 OR q3 = 4 AND leastC = 1 THEN
             ctB = 0
             FOR i = 1 TO 8
              IF q(i) = 2 THEN ctB = ctB + 1
             NEXT
             IF ctB = q4 THEN
               ctCB = 0
               FOR i = 2 TO 8 STEP 2
                 IF q(i) = 2 OR q(i) = 3 THEN ctCB = ctCB + 1
               NEXT
               IF q5 = 1 AND ctCB = 1 OR q5 = 2 AND ctCB = 3 OR q5 = 3 AND ctCB = 0 OR q5 = 4 AND ctCB = 2 THEN
                 lastA = 0
                 FOR i = 1 TO 8
                   IF q(i) = 1 THEN lastA = i
                 NEXT
                 IF lastA = 6 AND q6 = 1 OR lastA = 7 AND q6 = 2 OR lastA = 5 AND q6 = 3 OR lastA = 8 AND q6 = 4 THEN
                   ctDD = 0
                   FOR i = 2 TO 8
                     IF q(i - 1) = 4 AND q(i) = 4 THEN ctDD = ctDD + 1
                   NEXT
                   IF 1 = 1 THEN
                  ' IF q7 = 1 AND ctDD = 2 OR q7 = 2 AND ctDD = 0 OR q7 = 3 AND ctDD = 1 OR q7 = 4 AND ctDD = 3 THEN
                     REDIM ctA(4)
                     FOR i = 1 TO 8
                       ctA(q(i)) = ctA(q(i)) + 1
                     NEXT
                     ctr3 = 0
                     FOR i = 1 TO 4
                       IF ctA(i) = 3 THEN the3 = i: ctr3 = ctr3 + 1
                     NEXT
                     IF ctr3 = 1 THEN
                       IF q8 = 1 AND the3 = 3 OR q8 = 2 AND the3 = 4 OR q8 = 3 AND the3 = 2 OR q8 = 4 AND the3 = 1 THEN
                         FOR i = 1 TO 8
                          PRINT i, MID$("ABCD", q(i), 1)
                         NEXT
                       END IF
                     END IF
                   END IF
                 END IF
               END IF
             END IF
           END IF
         NEXT
        NEXT
      NEXT
    NEXT
  NEXT
NEXT


  Posted by Charlie on 2003-06-07 06:12:31
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