21-110: Problem Solving in Recreational Mathematics
Challenge questions: Friday, February 5, 2010
Question 1. In the course of adding two numbers, sometimes it is necessary to carry a 1. Explain
why it is never necessary to carry a 2.
Question 2. In the c

21-110: Problem Solving in Recreational Mathematics
Homework assignment 4 solutions
Problem 1. Recall that n!, read n factorial, is the number n (n 1) (n 2) 3 2 1.
For example, 5! = 5 4 3 2 1 = 120. The number 110! ends with a bunch of zeroes. How
many?
S

21-110: Problem Solving in Recreational Mathematics
Homework assignment 1 solutions
Problem 1. Find my oce. Sign your name on the sheet posted outside my oce door.
Solution. My oce is in the Physical Plant Building (PPB), room 342. One way to get there is

21-110: Problem Solving in Recreational Mathematics
Homework assignment 3 solutions
Problem 1. (A Swimmer and a Hat, from The Moscow Puzzles by Boris A. Kordemsky, edited
by Martin Gardner.) A boat is being carried away by a current. A man jumps out and s

Sometimes it is necessary to add long strings of numbers without a calculator. For example,
one might be asked to find 48 + 33 + 52 + 11 + 17 . This sum is difficult to compute without a
calculator, but the task can be made a lot easier by knowing some si

18.01 Calculus
Jason Starr
Fall 2005
Lecture 15. October 18, 2005
Homework. Problem Set 4 Part I: (d) and (e); Part II: Problem 2.
Practice Problems. Course Reader: 3B6, 3C2, 3C3, 3C4, 3C6.
1. The Riemann sum for the exponential function. The problem is t

21-110: Problem Solving in Recreational Mathematics
Section A, spring 2010, 9 units
Syllabus
Time and place: Mondays, Wednesdays, and Fridays, 1:302:20 p.m., in Porter Hall A22
Textbooks: Problem Solving Through Recreational Mathematics, by Bonnie Averbac

21-110: Polyominoes
Introduction
Take a sheet of graph paper (the bigger the squares, the better). What shapes
can you cut out using the squares?
A domino is a shape made from two adjacent squares. These are dominoes:
By modifying the word domino, we can

21-110: Problem Solving in Recreational Mathematics
Algebra puzzles
Wednesday, February 3, 2010
(Problems from The Moscow Puzzles by Boris A. Kordemsky, edited by Martin Gardner.)
Problem 37. The Price of a Book. A book costs $1 plus half its price. How m

21-110: Symmetry and tilings
Symmetry
Symmetry is a very important concept in mathematics. A large part of
mathematics is the identification and exploration of patterns, and symmetry is a
pattern that appears over and over again in many places.
Here we wi

21-110: Working systematically
Introduction
We often want to make a complete list of all of the different types of some
object, or search for a solution to a puzzle by trial and error. A very helpful
technique to follow in cases such as these is to work s

21-110: Problem Solving in Recreational Mathematics
Homework assignment 2 solutions
Problem 1. Suppose you have one copy of each free hexomino. Prove that it is impossible to
arrange them into a rectangle.
Solution. There are 35 free hexominoes. Each hexo