1) A polygon has n sides. If one of its interior angles is 84 deg, and the other interior angles are each equal to 156 deg, find n.
2a) If a product of two positive integers is a prime number, what must be the value of the smaller integer?
2b) Given that x and y are positive integers, solve x^squared - y^squared = 13
3) Given that 950k is a perfect cube, find the smallest possible value of k.
Please include workings. Very grateful for your help.
Here are some problems for maths geniuses
1. Catie placed the numbers 1 to 5 in the squares of the letter C, so the sum of the 2 numbers in the top row was the same as the sum of the two numbers in the bottom row, and the same as the sum of the three no. in the column. Show every possible way Catie could've placed the numbers and explain why there are no more solutions.
2. Mary's photocopier has seven buttons letting her reduce or enlarge the area of a printed image:
a) Mary wants to enlarge a picture. She does not want to copy more than 3 times. What is the closet she can get to an enlargement of 200%
b) Using just 4 of its 7 buttons and making copies of copies of necessary, Mary's phtocopier can produce the same size images as the complete set of seven buttons. Find 2 sets of 4 buttons with this property.