Multi-Balance Puzzles

Put the digits 1-n, each used exactly once, into the grid so that:

1) no row or column contains exactly one digit,
2) every row or column that contains 2 or more digits contains exactly one fulcrum,
3) each fulcrum is used horizontally or vertically, but not both, and
4) each fulcrum is located where those weights would balance, with equal torques on both sides.

A solved puzzle using the digits 1-6 is shown to the right:

Each puzzle below has a unique solution. All puzzles copyright Erich Friedman, 2010.


digits 1-6:

digits 1-7:

digits 1-8:

digits 1-8:

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