Problem One: Consider the top image below consisting of eight triangles. Remove four small triangle lines (no big lines) to leave only four small triangles. To complete this successfully, you must only have small triangles in your answer. No other shapes are permitted and no leftover lines may remain. Each remaining line must form an edge of the triangle.
Problem Two: Aunt Agatha's Haunted Mansions second floor landing consists of sixteen tiles arranged in a square. As you step on a tile, the tile will begin to dissapear underneath your feet. There is however enough time to make it to an adjacent tile. To cross the room and unlock the door on the opposite side (NOT diagonally opposite), you must step on all sixteen tiles. Remember, you cannot step on the same tile twice. No diagonal manovers allowed, there is not enough time. Question: how many ways are there to cross the room? See the diagram for one possible option.
Problem Three (i just made it up now, so its not that great):
Which value of n will make the following equation true?
2^(n-1) = 2n-1 = n^2 = 1/n
I haven't implemented any scoring system, but these are just an example.
I know that some of these are not directly math related and a bit more logic/lateral thinking
Poll: Who likes the "background" for question two? Would you like to see this or leave it out. Does it clutter the question, or give it atmosphere?
Just for fun, not a competition now guys!
Problem Two: Aunt Agatha's Haunted Mansions second floor landing consists of sixteen tiles arranged in a square. As you step on a tile, the tile will begin to dissapear underneath your feet. There is however enough time to make it to an adjacent tile. To cross the room and unlock the door on the opposite side (NOT diagonally opposite), you must step on all sixteen tiles. Remember, you cannot step on the same tile twice. No diagonal manovers allowed, there is not enough time. Question: how many ways are there to cross the room? See the diagram for one possible option.
Problem Three (i just made it up now, so its not that great):
Which value of n will make the following equation true?
2^(n-1) = 2n-1 = n^2 = 1/n
I haven't implemented any scoring system, but these are just an example.
I know that some of these are not directly math related and a bit more logic/lateral thinking
Poll: Who likes the "background" for question two? Would you like to see this or leave it out. Does it clutter the question, or give it atmosphere?
Just for fun, not a competition now guys!
