Hint: Convert the letters to positions of the alphabet.
The letters' positions in the alphabet are perfect squares.
Y = 25
P = 16
I = 9
D = 4
A = 1.
If you were given a one foot square piece of paper, could you cut a hole large enough to walk through?
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Fold the paper in half, make cuts reaching almost across the whole width of the paper, alternating from side to side. When the paper is opened, it makes a very large loop. Here is a template which would work:
What is the smallest integer, which, when multiplied by 7 gives a number consisting of only 6's?
If you have a helium filled balloon in a closed car, and you go around corner.
Will the balloon swing into or out of the corner?
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Hint: Does it matter that helium is lighter than air?
Answer: Into the corner.
As the car goes into the corner everything will be forced to one side, the outside of the corner. However, as helium is lighter than air, the air will go into the outside of the corner pushing the balloon the opposite way.