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Sam Again

Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.

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Pick

Investigate polygons with all the vertices on the lattice points of a grid. For each polygon, work out the area A, the number B of points on the boundary and the number of points (I) inside the polygon. Can you find a formula connecting A, B and I?

Good Work If You Can Get It

Age 11 to 14 Challenge Level:

A job needs three men to work for two weeks ($10$ working days).

Andy works for all $10$ days.
Bert works for the first week and Clive works for the second week.
Dave works for $6$ days, but then is too sick to work.
Eddy takes his place for $3$ days, then Fred does the last day.

money

When the job is finished they are all paid the same amount. At first they could not work out how much each man should have, but then Fred says:

"If I give my wages to Andy, and Eddy gives £$100$ to both Dave and me, then the wages will be correct".

How much was paid for the whole job, and how much does each man get?