# The questions of the history quiz

Here's an old puzzle I found on an 80's magazine. I slightly adapted it for Puzzling:

Four students, Anne, John, Philip and Daisy made an history test and gave the next four answers each to four questions, a), b),c) and d), about the dates of four important worldly historic events:

When the teacher evaluated the four tests, she realized that each student got, at least, one right answer and all of them had the same score (each question worth the same score).

What is the right answer to each question? And how many answers did each student got right? Oh! And by the way, maybe you'll be interested on assigning each date to an important historic event (not mandatory to solve the puzzle)...

• Was each question answered correctly at least once? (I assume so, or we'd never be able to say what the correct answer was to that question.) Should we also assume no two questions have the same answer? Nov 4 '20 at 9:10
• @JaapScherphuis, yes. Each question was answered correctly at least one time. It says so on the problem. And yes. No two questions have the same answer. I didn't refer that but that's kind of implied, don't you think?
– Pspl
Nov 4 '20 at 9:20
• I don't see where in the problem it says each question was answered correctly at least once, only that each student got at least one correct answer. But maybe the fact that all the answers must be different forces the issue. Nov 4 '20 at 9:25
• @JaapScherphuis, you should win a nobel prize!! You're right!! But the information I gave is enough to solve the problem!!
– Pspl
Nov 4 '20 at 9:28
• @Pspl. No, it's not. Just by the rules given, a valid answer is a) 1789, b) ??? c) ??? d) 1789. All students got 1 right, and got the same score (1). Nov 4 '20 at 17:25

a) 1760, b) 1939, c) 1914, d) 1789 correct answers, they all got 2 correctly. Also Anne got a and d right, John got c and d, Phillip got b and d and Daisy got b and c.

History facts:

1760 when George III takes the throne in Britain. 1789 George Washington becomes president of the USA. Haha relevant. 1914 WW1 starts. 1939 WW2 starts.

Another idea...

They each got one answer right: 1760

1. 1760 (When was the Battle of Wandiwash?)
2. 1760 (When did George II of Great Britain die and George III take the throne?)
3. 1760 (When was Pope Leo XII Born?)
4. 1760 (When was the Siege of Quebec?)

Anne got (a), John got (b), Philip got (c) and Daisy got (d) right.

I'll explain why Prince's answer is unique, assuming that each question has a different correct answer. Even though this assumption wasn't stated in the question (which is a bit confusingly worded in my opinion), it seems reasonable and leads to a unique answer so I think it was intended by the original puzzle creator. (And as OP stated in the comments, we don't need to assume that each question was answered correctly by at least one person.)

First, suppose that the answer to (d) is not 1789, meaning that Anne, John and Philip all got it wrong. Since Anne, John and Philip all gave different answers for each of (a), (b), and (c), they must each have gotten exactly one question right. The only ways to assign answers to these three are:
(a) 1760, (b) 1939, (c) 1914;
(a) 1939, (b) 1914, (c) 1760; or
(a) 1914, (b) 1760, (c) 1939.
In all these cases 1760 is the answer to (a), (b), or (c), meaning that Daisy got (d) wrong. But then in all three cases Daisy has either 0 or 2 correct answers.

So the answer to (d) must be 1789. For Daisy to get a correct answer, either (b) is 1939 or (c) is 1914. In each case respectively Philip or John has 2 correct answers, so everyone must have 2 correct answers. Therefore we need both (b) 1939 and (c) 1914, and to finish it off (a) is 1760 in agreement with Prince's answer.

Yet another idea...

Note that the question does not state that the answers are different for each question. With this, they could each have one answer right:
a. 1914
b. 1760
c. 1939
d. 1760
Who got what right: Anne - c, John - b, Philip - a, Daisy - d