50 428
Assignments Done
97,5%
Successfully Done
In July 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Get a free quote.
Check the website
Easy as ABC!
Just provide us with clear instructions and wait for the completed assignment.

# How to Get 100 With Nine Different Figures

There are a lot of different math tricks that can impress you with their beauty and compactness. In this post, you will find not only their examples but also will try to create your own. To begin with, a few “Mathematical Curiosities” are introduced by the famous Russian mathematician and physicist Yakov Perelman (1882-1942) in his popular book “Arithmetic for entertainment”. Here are some of them:

@$1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 × 9 = 100@$
@$12 + 3 – 4 + 5 + 67 + 8 + 9 = 100@$
@$123 – 45 – 67 + 89 = 100@$
@$24 \frac{3}{6} + 75 \frac{9}{18} = 100@$
@$94 + 157\frac{8}{263} = 100@$

In each of these expressions, we obtain the number 100 by operating with the nine natural numbers from 1 to 9 in different mathematical methods . Let’s now try to do something similar, formulating the problem in the following way:

Arrange symbols of the four arithmetic operations @$+, -, ×, ÷@$  in a row of numbers @$1, 2, 3, 4, 5, 6, 7, 8, 9@$ in any place (or don’t put anything, forming a double-digit, three-digit number, etc.) in such way that the obtained value  is equal to 100. Using other characters and operations (braces, root signs, powers, etc.) is not allowed.

Here are 101 solutions to this problem, grouped by a set of the operations performed.

@$123 + 45 – 67 + 8 – 9 = 100@$
@$123 + 4 – 5 + 67 – 89 = 100@$
@$123 – 45 – 67 + 89 = 100@$
@$123 – 4 – 5 – 6 – 7 + 8 – 9 = 100@$
@$12 + 3 + 4 + 5 – 6 – 7 + 89 = 100@$
@$12 + 3 – 4 + 5 + 67 + 8 + 9 = 100@$
@$12 – 3 – 4 + 5 – 6 + 7 + 89 = 100@$
@$1 + 23 – 4 + 56 + 7 + 8 + 9 = 100@$
@$1 + 23 – 4 + 5 + 6 + 78 – 9 = 100@$
@$1 + 2 + 34 – 5 + 67 – 8 + 9 = 100@$
@$1 + 2 + 3 – 4 + 5 + 6 + 78 + 9 = 100@$

@$12 + 34 + 5 × 6 + 7 + 8 + 9 = 100\\12 + 3 × 4 + 5 + 6 + 7 × 8 + 9 = 100@$
@$1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 × 9 = 100@$
@$1 + 2 × 3 + 4 + 5 + 67 + 8 + 9 = 100@$
@$1 × 2 + 34 + 5 + 6 × 7 + 8 + 9 = 100@$
@$1 × 2 × 3 + 4 + 5 + 6 + 7 + 8 × 9 = 100@$
@$1 × 2 × 3 × 4 + 5 + 6 + 7 × 8 + 9 = 100@$

@$12 + 3 + 4 – 56 ÷ 7 + 89 = 100@$

@$1 + 234 × 5 × 6 ÷ 78 + 9 = 100\\1 + 2 + 3 × 4 × 5 ÷ 6 + 78 + 9 = 100\\1 + 2 × 3 × 4 × 5 ÷ 6 + 7 + 8 × 9 = 100\\1 × 23 + 4 + 56 ÷ 7 × 8 + 9 = 100\\1 × 2 ÷ 3 + 4 × 5 ÷ 6 + 7 +89 = 100\\1 ÷ 2 × 3 ÷ 4 × 56 + 7 + 8 × 9 = 100\\1 ÷ 2 ÷ 3 × 456 + 7 + 8 + 9 = 100@$

## Addition, subtraction, multiplication and division

@$12 ÷ 3 + 4 × 5 – 6 – 7 + 89 = 100\\12 ÷ 3 + 4 × 5 × 6 – 7 – 8 – 9 = 100\\12 ÷ 3 + 4 × 5 × 6 × 7 ÷ 8 – 9 = 100\\12 ÷ 3 ÷ 4 + 5 × 6 + 78 – 9 = 100\\1 + 234 × 5 ÷ 6 – 7 – 89 = 100\\1 + 23 – 4 + 56 ÷ 7 + 8 × 9 = 100\\1 + 23 × 4 + 56 ÷ 7 + 8 – 9 = 100\\1 + 2 + 3 × 4 × 56 ÷ 7 – 8 + 9 = 100\\1 + 2 × 3 – 4 + 56 ÷ 7 + 89 = 100\\1 – 2 – 3 + 4 × 56 ÷ 7 + 8 × 9 = 100\\1 × 23 – 4 – 56 ÷ 7 + 89 = 100\\1 × 23 × 4 – 56 ÷ 7 ÷ 8 + 9 = 100\\1 × 2 + 34 – 56 ÷ 7 + 8 × 9 = 100\\1 × 2 – 3 + 4 + 56 ÷ 7 + 89 = 100\\1 ÷ 2 × 34 – 5 + 6 – 7 + 89 = 100@$

These 101 ratios apparently are a comprehensive solution of the problem posed at the beginning. However, if you change the initial conditions, then, of course, other solutions are possible. Consider some of the possible cases and golve them!

## Using parentheses:

@$(1 + 2 – 3 – 4) × (5 – 6 – 7 – 8 – 9) = 100\\(1 ÷ 2 – 3) × 4 ÷ 5 + 6 + 7 + 89 = 100\\(1 + 2 + 3 – 4 + 5) ÷ 6 × 78 + 9 = 100\\1 × (2 + 3) × 4 × 5 × (6 – 7) × (8 – 9) =100@$

## Adding a minus in front of the unit:

@$–123 – 4 + 5 × 6 × 7 + 8 + 9 = 100\\–123 + 45 × 6 – 7 × 8 + 9 = 100 \\–1 ÷ 2 – 3 + 45 ÷ 6 + 7 + 89 = 100 \\–1 ÷ 2 × 34 + 5 × 6 + 78 + 9 = 100@$

@$(–1 + 23) × 4 ÷ 56 × 7 + 89 = 100\\((–1 × 2 ÷ 3 – 4) × 5 ÷ 6 + 7 + 8) × 9 = 100@$
@$123 – 4 + 5 – 6 – 7 – 8 – \sqrt{9} = 100@$
@$123 – 4 – 5 – [6.7] – [8,9] = 100@$
@$1 + 2 + 3 + 4 + 5! – 6 – 7 – 8 – 9 = 100@$