2006 U. S. Championship Puzzles

1. Warm-Up

What is the next number in this series?

10, 9, 60, 90, 70, ?

2. Slide Weights

The weights in the following puzzles have whole number weights 1 to n. Determine which weights must be placed in the places shown so that there is equal torque on both sides of every horizontal bar. Each weight must move 1/2 unit either left or right in the final answer.

3. Hex House

Draw a path through all the empty hexes. Your path must visit each hex only once, and change direction only when it hits the edge of the grid, itself, or one of the black hexes.

4. Distance

Place the numbers 1 through 13 in the circles so that the distance between successive pairs of consecutive integers increases.

5. Pentomino Puddles

Divide each of the regions given into 3 parts so that the 12 parts are the 12 different pentominoes.

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