#1




Liars!!!
First, Second and Third,Three lifelong rivals, have challenged one another in a sprint. Each of them put all their effort into the race. You later met them and regrettably asked them who won the race. They each gave two statements about the results of the race but you know that for two of them one statement must be true and one statement must be false. However the third person's statements are always false. Their statements were as follows:
First:" I am First and Third is second". Second:"Third is third and i am first". Third:"Second is third and First is second". Determine the true result of the race. 
#2




The actual result is the same as the order you ask them. Since we know that two of three give one true (T) and one false (F) statement, and one of them gives two false statements, it can be shown as such:
First: "I am First (T) and Third is second (F)." Second: "Third is third (T) and I am first (F)." Third: "Second is third (F) and First is second (F)." From First, we know that First is first/First (whether it's the position or the name, it works) and Third is not second. Since First is first and Third is not second, Third must be third. From Second, we know that Third is third (which confirms what we know from First) and that Second is not first, meaning that Second must be second. From Third, we know that Second isn't third (because they are second) and First is not second (because they are first). Therefore, First, Second, and Third finished first, second, and third, respectively. 
#3




1st, 2nd, 3rd or 2nd, 3rd,1st

#4




Yes, you are both correct

#5




The challenge was to determine the true result of the race.
The correct answer is, it is indeterminant, because there are two possible results that satisfy the conditions. 
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