I'm interested in
>>18's surefire 2 attempt solution. Here's mine, modified for twelve fixed questions in the example.
1. Set the first half of the problems false and the second half of the problems true; if the answer is less than half correct, switch them around.
2-x. Over a period of tests, change answers in both the first half and the second half of the test then submit.
: If the correct result count goes down, both original values are correct.
: If the count goes up, both of the new values are correct.
: If the count stays the same, only one of those new values was correct and you can figure out which by process of elimination:
In the following case, in step 1, only one is correct; in step 2, keeping the first one the same proves that the second is false.
A T || T T
B F || T F
C T || T
In the following case, in step 1, only one is correct; in step 2, we have one correct, which means A and B are still both false a C is correct (if we had have none correct, all the answers would be inverted).
A F || T T F
B T || T F T
C T || T T
In the following case, in step 1, only one is correct; in step 2, keeping the first value the same only equals one more correct result; this means we know C is actually false.
A T || T T T
B F || T F F
C F || T F
Example:
0 1 2 3 4 5 6 7 8
T || F T -F- -T- T T T T T
T || F T T -F- T T T T T
F || F T T T -F- F F F F
T || F T T T T -F- T T T
F || F T T T T T -F- -F- F
F || F T T T T T T -F- F
T || T F -T- (T) T T T T T
T || T F F F -T- T T T T
F || T F F F F -T- F F F
F || T F F F F F -T- (T) F
F || T F F F F F F F F
F || T F F F F F F F F
Note: -#- means the value has changed, (#) means this number was unchanged and is being tested this turn; by step 7, we have verified all 5 true values and solved the test in submission 8 (confirmation in 7/12 time, success in 2/3 time, less than 5/6 time).
This example forces us to test our numbers every other turn until we have verified the full first half:
0 1 2 3 4 5 6 7 8 9 10
T || T -F- -T- T T T T T T T
F || T T -F- F F F F F F F
T || T T T -F- -T- T T T T T
F || T T T T -F- F F F F F
T || T T T T T -F- -T- T T T
F || T T T T T T -F- F F F
T || F -T- (T) T T T T T T T
F || F F F -T- (T) F F F F F
T || F F F F F -T- (T) T T T
F || F F F F F F F -T- F F
F || F F F F F F F F -T- F
T || F F F F F F F F F T
We get our answer in 5/6 time the worst case example.