# Should students get another chance at a math question because of English troubles?

The question is John has locked a 4 digit combination lock with each of the numbers 0-9. He knows the numbers 1,4,6, appears exactly once, but he does not remember the position of the numbers and he is not sure of what the fourth number is.

The student think the fourth number is the number in the fourth position of the combination lock. He thinks so because people do not say an order of the number you know or not know. So later I wanted him to try again with the right idea. There are two students who thought this way. The students first language is not English. I would let them try again since its not a math issue and would you? Also can it also be interpreted this way?

• If the question is worded exactly as you've given it (has several ambiguities, some grammar errors, etc.), I would be very generous with complaints by students. Teachers should have sufficient command of the subject matter and writing questions to anticipate (and thus avoid) these type of issues when writing questions. For example, since the combinations are "4 digit numbers", it is reasonable to assume $0$ cannot be the left-most digit, but then you say "each of the numbers 0-9", which suggests otherwise. – Dave L Renfro Oct 7 '20 at 9:12
• FYI, the following is less ambiguous: The correct combination to John’s lock consists of $4$ digits in a certain order and each chosen from $0$ through $9,$ any or all of which can be repeated. John does not completely remember the correct combination, but he does know that each of the digits $1,$ $4,$ and $6$ appears exactly once. The answer to the presumed question that follows is $(4)(3!)(7),$ as there are $4$ locations to put the three known digits, $3!$ ways to permute the three known digits, and $7$ possibilities for choosing the remaining digit (whose location is now fixed). – Dave L Renfro Oct 7 '20 at 9:42
• Yes, I think it is justified. If you are writing the questions, and you find it difficult to avoid issues like this (and they will be difficult until you get more question writing practice and teaching experience), my advice would be to include some examples, which in this case could be $0416$ and $0461$ and $6184$ as consistent with what John knows, and $4116$ and $2356$ as inconsistent with what John knows. (This many examples might be overkill, however.) – Dave L Renfro Oct 7 '20 at 9:53
• any or all of which can be repeated --- In looking at this 7 hours later, I see that there is a slight ambiguity even in what I wrote: Does "repeated" mean exactly two occurrences or two or more occurrences? I suppose one could write "any or all of which can be repeated one or more times", but now the verbiage might start playing a nontrivial role in solving the item (especially for ESL students). However, this particular ambiguity doesn't arise if the student understands the other constraints. – Dave L Renfro Oct 7 '20 at 16:54
• Yes, it can be interpreted in the student's way. You wrote "but he does not remember the position of the numbers and he is not sure of what the fourth number is". The word "position" occurs in this sentence, followed by "fourth", so a reasonable interpretation is that "fourth" refers to the position of the number, and not the remaining number. There are two orders, the order of the digits in the combination lock and the order you used when speaking about the digits. If someone isn't sure which order you meant, then isn't it reasonable to assume you meant the most recently mentioned order? – Dave L Renfro Oct 14 '20 at 9:45