1) Using a compass, and a straight edge( with no marks). Construct 4 points such that when you connect them, they would form a square.(adsbygoogle = window.adsbygoogle || []).push({});

2) Find all prime p such that 17p+1 is a perfect square.

3) You are in a island with three kinds of people.

Normal: might or might not lie.

knight: Always do the right thing, and tell the turth.

lier: That is obvious.

Suppose you encounter two person walking side-by-side in this island( label them A, and B). You go up to Person A, armed with a single question to ask A, you corructly deduce the identity of Person B. What is that unique question?

4) Suppose you have a 6 digit number. Suppose you switch the first 3 digit of that number to the last three digits of that number; the new number would be six times the original number. Obviously, my question is what is that number?

5) (x^2) + ( y^2) + 1 = (z^2) prove infinite many integer solution.

6) Last three digits of 3^4798?

7) You have a u shape tude. The open ends of the tude have the same cross sectional area, and is pointing up. Water is pored into the tude until the water level is M above the ground. Now, if i pore some oil in to the right side of the tude, obviously, the water level on the left side of tude would rise by some number h, because of the inclusion of the oil. What is the height of the oil-air interface on the right side of the tude? what is the height of the water-oil interface on the right side of the tude? Intruduce more stuff if you need to.

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