Complicated Euler

This is a do it yourself, although you can still answer the question (is it possible) in the comments below. Can you trace along all of the lines, without lifting the pen from the paper and tracing each line only once?

If you need a hint, this is a rather complicated Euler puzzle.

Don't forget to let us know if you were able to do it!





UPDATE: SPOILER ALERT!!!!!!!!!!!!!!!!!!!!!! Scroll down if you want to see a possible solution.  It's not the only one, but it does work.













 

Follow the nodes around starting at 1, then move to 2, 3, 4, etc...  You'll notice there are two odd nodes with three numbers.  Start at the first odd node and end at the other to solve.

Football puzzle

I'm still tired and cranky from last night's game. So here's a football puzzle for you. How many different ways can you score 20 points in a football game?

Assume the following possibilities for scoring:

• If the other team doesn't show up, the game is forfeit, and you score 1 point (and the game is over.)
• On defense, if you tackle the other team's quarterback in their endzone, you get 2 points for a "safety".
• On offense, you can kick the ball over the defense's goalposts for a 3 point field goal.
• On offense, you can carry the ball across the defense's goal line for a 6 point touchdown.
• On offense, immediately after a touchdown, you can kick the ball through the defense's goalposts for an additional 1 point ("point after touchdown"). We can combine this with the touchdown and write it as a (6+1) or 7 point score.
• On offense, immediately after a touchdown, you can make another play to carry the ball across the defense's goal line for an additional 2 points ("two point conversion"). We can combine this with the touchdown and write it as a (6+2) or 8 point score.

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