# True-False Examination

Alice, Bob, Chloe and David took a 10 question true-false exam; every correct answer of a question is $1$ point.

Their answer sheet and the result is shown as below: So what is David's total number of points?

    A   B   C   D
1   T   T   F   F
2   F   T   T   F
3   F   F   T   T
4   T   F   T   T
5   T   T   T   F
6   F   F   F   T
7   T   T   T   T
8   F   F   T   T
9   T   F   F   F
10  F   T   F   T
TP  8   4   7   ?

• The way the question is asked they should all have 10 points because it says each question is one point. It does not say each correct answer is one point. – user42273 Nov 13 '17 at 16:03
• @user42273 I will fix it thanks! :) – Oray Nov 13 '17 at 17:35

B differs from A in only 4 places, and has 4 fewer correct answers, so in those places we know A is correct: 2 is false, 4 true, 9 true, 10 false.

We can remove these rows from the table and adjust the totals on the remaining questions:

    A   B   C   D
1   T   T   F   F
3   F   F   T   T
5   T   T   T   F
6   F   F   F   T
7   T   T   T   T
8   F   F   T   T
TP  4   4   5   ?-2


C and A differ in 3 places (1,3,8); A is correct for one of them, and C is correct for two of them, as this is the only way to account for the difference in their scores on the sub-exam. D agrees with C for all three of these, so D is also correct for two of (1,3,8). We know that 5 is true, 6 false, and 7 true, so D gets 1 point from these three questions as well.

D has 3 total questions correct on this sub-exam, and so D has a total score of 5 on the test.

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

• this is not necessarily true. – Oray Nov 13 '17 at 17:01
• so they're hyopthetical answers, and can still be used to solve the puzzle assuming it is well-formed and has a single answer. – Jasen Nov 14 '17 at 9:39