## 5. Puzzles

• These puzzles have been collected from a number of sources to help build problem solving skills, primarily for design.

• In most/all cases the problems have been rewritten to appeal to the engineering approach to problems.

5.1 Math

• We are planning to build a new autoparts factory to supply stores along a straight section of highway. It doesn’t matter where we build the factory, except the total driving distance will vary. We want to choose a location that minimizes the total driving time. Each grid space below represents 10 miles. [Carter & Russell, 1995] • A customer has indicated that 10 years from now four inventory items will be a total of 100 years old. What will their total age be 7 years from now? [Carter & Russell, 1995]

• The Towers of Hanoi is a classic puzzle that requires that discs of smaller sizes be moved one piece at a time to the other posts, while never putting a larger disc over a smaller one. In the case below the discs are on one post. How many moves are required to move all of the discs to another post? • Nellie the pig can eat a trough of slop in 2 hours. Billie the pig can each a trough of slop in 1.5 hours. How long would it take both of the pigs together to eat one trough of slop?

• A total of 35,555 marbles were dropped in a tank, and sorted into four sizes. We missed the count of the first bin, but the second bin was 2,384 marbles less, the third was 5,285 less, and the last was 8,923 less. How many were in the first bin?

• A lineup was used to check three automobile safety systems. The tally sheets indicated the numbers below. How many cars had only one safety system working? • If a train is half a mile long, and enters a tunnel that is 3 miles long, how long will some part of the train be in the tunnel if the train is travelling at 55 m.p.h.?

• Using one stroke of a pen, make the following equation true, • Add plus/minus signs to the left hand side of the equation below to balance the equation, 5.2 Strategy

• Using six equal size sticks, create three squares of equal size.

• Divide the rectangle into three pieces that will make a cross, • We have four sticks of equal length, and four more sticks that are twice as long. Move the sticks to make four squares of the same size.

• Cut the cross below into four identical pieces that can be rearranged into a square [Carter & Russell, 1995] • Move four matches to make three equilateral triangles • Chess Stuff: Move a night about a chessboard so that in 16 moves it touches all of the squares on the board. Move a bishop around a board to touch all black squares in 17 moves. Move the queen about the board to touch all the squares in 14 moves. [pentagram]

• How many balls can be removed from the box below, while still leaving the others locked in place? [Pentagram] 5.3 Geometry

• Consider the associations below, • Find all of the triangles of different sizes in the figure below. [Pentagram] • Rearrange the shapes below into three equal shaped smaller six pointed stars, 5.4 Planning and Design

• How can a brick be suspended with a single sheet of paper.

• Why are manhole covers round.

• Put a marble on a table. Using only a glass remove the marble from the table (without touching it).

• Draw lines that do not cross between boxes containing the same letters. 5.5 References

5.1 Carter, P., and Russell, K., IQ Puzzles; Beat The Mensa Puzzlemasters, Robinson Publishing, London, England, 1995.

5.2 Pentagram, More Puzzlegrams, Simon & Schuster Inc., New York, 1994.