Calculating with Roman numerals

Brain teaser with the help of the ancient Romans

Our decimal number system with Arabic numerals has many advantages. It makes the math pretty easy. But there were and are other types of number systems. The Roman number system was very well known and successful throughout history. After all, it helped organize and administer the Roman Empire for centuries. Today the numbers are mainly used as design elements or ornaments.

From our modern point of view, the numbers seem unwieldy, and the arithmetic is not so easy to understand.

But that’s precisely why beautiful brain teasers can be derived. When calculating with Roman numerals, you must “think outside the box”.

Try to solve the arithmetic problems with the Roman numerals in your head.

## Symbols of the Roman Numerals

As a reminder, we list the symbols and values in the Roman number system here:

I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000

## The subtraction rule

Note the subtraction rule: The numerals I, X and C may be placed in front of one of their two next larger numerals. The value must then be subtracted from the following value:

• I before V: IV stands for the value 4

• I before X: IX stands for the value 9

• X before L: XL stands for the value 40

• X before C: XC stands for the value 90

• C before D: CD stands for the value 400

• C before M: CM stands for the value 900

In each of the following equations a part is missing that must be calculated. That is not always the result on the right. In some cases, one of the operands is missing from the calculation on the left side.

More information about the Roman Numerals is available here.

In each of the following equations a part is missing that must be calculated. That is not always the result on the right. In some cases, one of the operands is missing from the calculation on the left side.

Calculate the result for this exercise: **IV – III = ___**

Solution:

**4 – 3 = 1** (With arabic numerals)

**IV – III = I** (With roman numerals)

## Brain Teasers with Roman Numerals

Try to solve the following exercises and equations:

Exercise 1:

**___ – II = VI**

## Solution 1

VIII – II = VI

Exercise 2:

**___ – XII = V**

## Solution 2

XVII – XII = V

Exercise 3:

**___ * IV = LX**

## Solution 3

XV * IV = LX

Exercise 4:

**V + XIX = ___**

## Solution 4

V + XIX = XXIV

Exercise 5:

**XIV – IX = ___**

## Solution 5

XIV – IX = V

Exercise 6:

**___ + IX = XX**

## Solution 6

XI + IX = XX

Exercise 7:

**XIII + ( XV + XVII ) = ___**

## Solution 7

XIII + ( XV + XVII ) = XLV

Exercise 8:

**V + XIX = ___**

## Solution 8

V + XIX = XXIV

Exercise 9:

**___ * VI – XIX = LIII**

## Solution 9

XII * VI – XIX = LIII

Exercise 10:

**( XIV + XX / V ) * ___ = CCCXLII**

## Solution 10

( XIV + XX / V ) * XIX = CCCXLII