arXiv:math/0312309v16 [math.GM] 4 May 2006
The Collatz 3n+1 Conjecture is Unprovable
Craig Alan Feinstein
May 4, 2006
Baltimore, Maryland U.S.A. email: [email protected], BSD
Disclaimer: This article was authored by Craig Alan Feinstein in his private capa
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Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer
Mini-Sudoku Puzzle
Complete entries in this
chart so that letters A-F
appear without repetition
in each row, each column
and each 2 3 block
Standard Sudoku consists of
a 9 9 chart, but this mini
version is good for a quick fix
USA Today carries a daily
mi
Word Search Puzzles
The puzzle below is a little harder than the normal word search:
one of the 36 first/last names has been left out (which one?)
Type 1, With Word List Supplied
AGITATOR
ASSEMBLY
CLUTCH
CONNECTORS
CONTROL
COUPLING
GLIDE
LINT SCREEN
PULLE
Rearranging Trains
Train cars
B
Engine
A
D
C
Track
Sorted order
D
C
B
A
Stub or lead
B
A
D
C
Stack or LIFO data structure in CE
B
A
D
C
Stub or lead
Stub or lead
C
A
B
D
Question: Is there an ordering that cannot be sorted using a stub?
Devising a sorting
Making Change: Ground Rules
For the sake of the puzzles in this presentation:
Coin means one of the pieces 1, 5, 10, 25 (no 50 or $1 coin)
Bill means one of the denominations $1, $5, $10, $20, $50, $100
Warm-up puzzle: What is the largest sum of coins tha
Houses and Utilities: Warm-up Version
There are n houses on one side of a street and 2 utility companies
on the other. Connect each utility facility to every house via lines of
any desired shape such that the lines do not intersect.
Problem interpretation
Finding an Impostor
There are three people of a certain profession (say, medical doctors)
in a room, but one of them may be an impostor. Each person asks the
other two a question that can determine whether the person is real.
The six yes (real) / no (impo
Easy: Euclid Sequences
Form a sequence of number pairs (integers) as follows:
Begin with any two positive numbers as the first pair
In each step, the next number pair consists of
(1) the smaller of the current pair of values, and (2) their difference
Stop
The Island of Liars and Truth-Tellers
Setting for puzzles in the next few slides:
You are on an island populated by two tribes.
Members of one tribe consistently lie.
Members of the other tribe always tell the truth.
Tribe members can recognize one anothe
Weighing with a Balance
A large container is known to hold 24 oz of nails.
The hardware store has a balance, but no weights.
Can you measure out 9 oz of nails for a customer?
A chemist has a balance and fixed weights of 1, 2, 4, and 8 grams.
Show that she
Behrooz Parhami
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Ten Puzzling Problems in Computer Engineering
Enrollment code: 10892
Research
Prerequisite: Open to (pre-)computer engineering students only
Computer arith
Behrooz Parhami
Home & Contact
Curriculum Vitae
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Ten Puzzling Problems in Computer Engineering, Spring 2009
Enrollment code: 10496
Research
Prerequisite: Open to (pre-)computer engineering students only
C
ECE 1: Computer Engineering Freshman Seminar
ECE 1: Previous Offerings of the Seminar
Behrooz Parhami: 2009/01/06 | E-mail: parhami at ece.ucsb.edu | Other contact info at: Bottom of this page
Go up to: B. Parhami's course syllabi or his home page
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IEEE TRANSACTIONS ON EDUCATION, VOL. 52, NO. 3, AUGUST 2009
Motivating Computer Engineering Freshmen Through
Mathematical and Logical Puzzles
Behrooz Parhami, Fellow, IEEE
AbstractAs in many other elds of science and technology, college students in co