The statement (*) is only true when Fred does at least one maths problem every day next week. Therefore, the statement (*) is false when Fred does no maths problems on at least one day next week.
First consider F. F states that on no day next week will Fred do no maths problems. This is the equivalent of "Fred will do at least one maths problem every day next week." Therefore this is equivalent to the statement (*).
Now consider A. A states that Fred will do more than one maths problem every day next week. If the statement (*) is true, A is true.
Then consider C. C states that on no day next week will Fred do more than one maths problem. Even if the statement (*) is false, C doesn't always hold true. This is because Fred could do no maths problems on some days, and more than one maths problem on other days.
To rule out B from being the correct answer, we could assume that Fred does no maths problems every day next week.
D is also not the correct answer. Even if Fred doesn't do at least one maths problem every day next week, he could still have done some maths problems on some days.
With all of the other choices eliminated, E is the only correct answer. The only way for Fred to not do at least one maths problem every day, as stated in the statement (*), is for Fred to do no maths problems on some days next week.