Vol. 8 No 7 - Pi Mu Epsilon

PUZZLE SECTION
Edited by
Jobeph V . E. Konhaube~
The PUZZLE SECTION is for the enjoyment of those readers who
are addicted to wrking doublecrostics or who find an occasional
mathematical puzzle attractive. We consider mathematical pussies to
be problems whose solutions consist of answers immediately recognisable
as correct by simple observation and requiring little formal proof.
Material submitted and not used here will be sent to the Problem Editor
if Seemed appropriate for the PROBLEM DEPARTMENT.
Address all proposed pussies and puzsle solutions to Professor
Joseph D. E. Kenhauser, Mathematics and Convputer Science Department,
Macalester College, St. Paul, Minnesota 55105. Deadlines for puzzles
appearing in the Fall Issue will be the next February 15, and for the
puzzles appearing in the Spring Issue will be the next September 15.
3. Phopobed by the EdLLtoh.
Bored in a calculus class, a student started to play with his
hand-held calculator. He entered a four-digit number and then pressed
the "square" key. To his surprise (and delight) the four terminal
digits of the result were the same digits in the same order as those in
the number which had been squared. What was that number? - -
4. Phopo~ed by the EcLitoh.
The side lengths of a convex quadrangle are positive integers
such that each divides the sum of the other three. Can the four side
lengths be different numbers?
5. Phopobed by the E&tOh.
If the four triangular faces of a tetrahedron have equal areas
must the faces be congruent?
region.
6. Phopohed by a vatchiebb wend.
Nine matchsticks are laid end-to-end to enclose a triangular
PUZZLES FOR SOLUTION
1. Pmpobed by John M. How&, Box 669, Li.ttiwck, CA.
Partition a regular hexagon into four congruent six-sided
figures .
Place two more matchsticks of the same length end-to-end inside the
triangle to bisect the triangular region.
In the triangular array
2. Phopohed by the Edt-toh.
A certain card shuffling device always rearranges the cards in
the same way (that is, the card in the ith position always goes into the
jth position, and so on). The Ace through King of Clubs are placed into
the shuffler in order with the Ace on the top and the King on the bottom.
After two shuffles the order of the cards - from top to bottom - is
What was the order of the cards after the first shuffle?
each number not in the top row is equal to the difference of the two
numbers above it. Are you able to arrange the integers 1 through 10
in a four-rowed triangular array with the same property? One through
15 in a five-rowed array? One through 21?
GRAFFITO
Mo one. -LA born knowing the. ,technique^ doh b0l~ing phobiesni and otheh
d X e m . 1.t -LA a ieahned b w and ghou &om bucc~bb6d expUiience.
Solving puzzle^ -LA one way to g& tfcc& expmience..
Jo~epfcuie and Richd V. Andhee
Logic uncocki