In a classroom, the teacher announces a prime number to a class of 10 students.The 10 students then each make one statement, in the following order:
Student 1: The number is greater that 1000
Student 2: Student 1 is telling the truth.
Student 3: If the number is greater than 1000000, Student 1 is lying.
Student 4: If the number is odd, Student 2 is lying.
Student 5: The number is greater than 10000000.
Student 6: The sum of the digits of the number is 27.
Student 7: If Student 4 is telling the truth, Student 6 is lying.
Student 8: The number can be expressed in the form for an integer .
Student 9: Student 3 is telling the truth if and only if Student 7 is lying.
Student 10: The number can be expressed as the sum of two perfect squares.
Let be the minimum number of students who could be telling the truth, and let be the maximum. Evaluate .
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
No explanations have been posted yet. Check back later!