A Tribute to Martin Gardner

[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

[TrevorW]

maths is a marvelous thing in some ways even beautiful it's just the understanding that makes it difficult at times

[gary]

Originally Posted by Robh

As a tribute to the memory of Martin Gardner (who passed away on May 22nd) ...

Hi Rob,

I appreciate your post as I had not heard the news that he had passed away
which saddens me to hear.

I always enjoyed reading his Mathematical Games articles in Scientific American
in the 60's and 70's and learnt a great deal from them. I still have a collection.

One of the other great contributors to that magazine in that era was C.L. Stong
who wrote the "Amateur Scientist" articles and he too passed away some time
back. When I was in high school, I wrote Stong a letter and he wrote back
a wonderful personally typed reply that must have been made on an old rickety
typewriter. His response was a joy to read and full of good humor and meant
a lot to me. The school library had two copies of his book which I would
have nearly on perpetual loan.

Best Regards

Gary

[Robh (Rob)]

Article on Martin Gardner in the Age ...
http://www.theage.com.au/world/mathe...0526-we1w.html

How to make a cyclic hexa tetraflexagon ...
http://www.youtube.com/watch?v=4DETMhTC0H0

Rob.