[Robh (Rob)]

As a tribute to the memory of Martin Gardner (who passed away on May 22nd), I've thought I'd put up a few mathematical puzzles for a rainy night.
Martin Gardner had a regular Mathematical Games section in Scientific American and published many books (including Fads and Fallacies in the Name of Science).

Some puzzles have multiple solutions.
Puzzle 5 is the hardest.

#1.
Using the numbers 1,2,3,4,5,6,7,8,9 in that order, insert either + or - signs to make an expression equal to 100.
Adjacent numbers can be annexed to make a two digit number.
e.g. 1+2-3+45+67+8-9 = 111, which is of course not the required answer.

See attached sheet:
#2.
Using all the numbers 1 to 12, place the numbers in the squares so that each straight row of four numbers adds to the same total.
The example on the sheet with these numbers
5 12 3 7
4 - - 1
10 - - 9
8 6 2 11
is of course not correct.

#3.
Start at one of the points A through to H and draw the shape shown on a blank piece of paper without taking your pen off the page. No segment already drawn can be traced over again.
If you were successful, at what point did you start and at what point did you finish?

#4.
Find the value of the altitude h (see sheet). The diagram shows three right-angles.

#5.
Find a set of integer (whole number) values for a,b,c,d which satisfy the conditions of the diagram.
e.g. a = 9, b = 12, c = 15 satisfy Pythagoras' Theorem as 9^2+12^2 = 81+144 = 225 and 15^2 = 225.
However the altitude d is not an integer for these values.
*What is the set of smallest integer values of a,b,c,d?

Enjoy!
Rob