 Number Sentences (Order of Operations Puzzles),
a selection of answers from the Dr. Math archives.
 Solving Number Sentences:
A Strategy
 I have been given a list of numbers without any plus or minus
signs and I have to place the signs between the digits.
 Order of Operations Problems 
a General Strategy
 Make equations using 7, 26, 46, and 15 to equal 160; 18, 9, 24,
and 20 to equal 18.
 A Bidirectional Search
 How can I get the numbers from 1100 using only four 8's?
 Order of Operations Puzzle
 What is _ + _ x _  _ = 22? We're given the numbers 2, 3, 4, 8.
 1 2 3 4 5 6 7 8 9 0 = 100
 Leave the numerals in this order. Place only addition and
subtraction signs to make it a true statement.
 Four 4's Puzzle
 How can you get 73 by using 4 fours and any mathematical equation?
 The Four Fours  an Ancient Problem
 The problem allows you to use only four fours and as many operands
as you like in order to create mathematical sums that equal the numbers
from 1 to as high as you can go.
 Four Four's, 210
 Find a numerical expression using four 4s for each integer
from 2 to 10.
 Four Twos Puzzle
 How can I get 15, 17, 19 and 21 using 4 twos?
 Two 2s Make 5
 Using only two 2s and any of the standard mathematical symbols, write
an expression whose value is equal to exactly five.
 Make 24
 We have to make 24 by using 1, 3, 4, and 6.
 Make 7,7,3,3 into 24 Using +  * and /
 Make the numbers 7,7,3,3 equal 24 using the operations addition,
subtraction, multiplication, and division.
 Twenty or Fewer Steps
 Only the 1, +, , x, /, (, ), and = keys on a scientific calculator
are working. How can a result of 75 be reached by pushing these keys
fewer than 20 times?
