Hi,
I cant figure out how to do these 2 problems without bashing. Do you guys have any ideas for an elegant solution? Thank you!
Prob 1.
An RSM sports field has a square shape. Poles with letters M, A, T, H are located at the corners of the square (see the diagram). During warm up, a student starts at any pole, runs to another pole along a side of the square or across the field along diagonal MT (only in the direction from M to T), then runs to another pole along a side of the square or along diagonal MT, and so on. The student cannot repeat a run along the same side/diagonal of the square in the same direction. For instance, she cannot run from M to A twice, but she can run from M to A and at some point from A to M. How many different ways are there to complete the warm up that includes all nine possible runs (see the diagram)? One possible way is M-A-T-H-M-H-T-A-M-T (picture attached)

Prob 2.
In the expression 5@5@5@5@5 you replace each of the four @ symbols with either +, or, or x, or . You can insert one or more pairs of parentheses to control the order of operations. Find the second least whole number that CANNOT be the value of the resulting expression. For example, each of the numbers 25=5+5+5+5+5 and 605+(5+5)×5+5 can be the value of the resulting expression.

Prob 3. (This isnt bashing I don't understand how to do it though)
Suppose BC = 3AB in rectangle ABCD. Points E and F are on side BC such that BE = EF = FC. Compute the sum of the degree measures of the four angles EAB, EAF, EAC, EAD.

P.S. These are from an RSM olympiad. The answers are