TRINITY MATH TRIATHLON

1.  Left to right:  Maria, Samuel, Lucy, Gayle, Mike, Gina

2.  Only three of the shapes can be created with a single slice of a square:  
Isosceles Triangle, Trapezoid, and Pentagon.  The others are impossible.

3.  

4.  (a)  Smallest positive integer creations:

(i)    1 = (-2)7 + (3) 5
(ii)   2 = (-2)6 + (1)14
(iii)  4 = (1)4 + (0)20
(iv)  1 = (-5)25 + (6)21

4. (b) the result is always the gcd of the two numbers

5.  The next five numbers that cannot be generated by any other positive integer are 3, 5, 7, 9, and 20.