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Number Sentences

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 1-100 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, 2-10

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?