Brain Teasers

1. Tangrams are an old Chinese game. They are a variation of a jigsaw
puzzle. There are 7 pieces that form a square. To make one, just cut out
a square piece of cardboard and mark off the diagonals. Also mark the
centres of two sides (marked as e and i in the figure). Find the mid-point
of each portion of the diagonal (marked c, f, g in the figure). Join the
appropriate points and cut out the 7 pieces as shown. There are two big
triangles, one medium triangle, two small triangles, one square, and
just one odd-shaped parallelogram.

Now, what is the brain teaser? Re-arrange the pieces to form a rectangle.

2. I just found a number with an interesting property:

 When I divide it by 2, the remainder is 1.
 When I divide it by 3, the remainder is 2.
 When I divide it by 4, the remainder is 3.
 When I divide it by 5, the remainder is 4.
 When I divide it by 6, the remainder is 5.
 When I divide it by 7, the remainder is 6.
 When I divide it by 8, the remainder is 7.
 When I divide it by 9, the remainder is 8.
 When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
Can you find it? (From Brainden.com)

Hint: If the number N gives 1 remainder when divided by 2, what is the
remainder for the number N+1?