Roman Numeral Twist

You probably already know about this; in fact, I numbered my number tricks with Roman numerals on the Math Trick Menu!

This is the Roman numeral for 4: IV

And this is the Roman numeral for 6: VI

And this is the Roman numeral for 9: IX

And this is the Roman numeral for 11: XI

And this is the Roman numeral for 40: XL

And this is the Roman numeral for 60: LX

And this is the Roman numeral for 90: XC

And this is the Roman numeral for 110: CX

And this is the Roman numeral for 400: CD

And this is the Roman numeral for 600: DC

And this is the Roman numeral for 900: CM

And this is the Roman numeral for 1,100: MC

Did you notice how the letters switched places for each 2nd numeral? I call this the Roman Numeral Twist!

You can use addition or subtraction to "twist" the numerals so the letters switch places! The number you must add or subtract is:

2 × 10^x

Or maybe since we're using Roman numerals, I should print it like this:

II * X^p

(I replaced the "x" multiplication symbol with an asterisk & the exponent variable "x" with a lowercase P to prevent confusion with the "X" Roman numeral for number 10.) The exponent must be an integer!

Do you understand the logic with the Roman numerals at the top of this Web page? The numbers 4, 6, 9 & 11 × 10 to the power of an integer of your choice is printed using this logic:

Subtract if the smaller numeral is at the left of the bigger one; add if the smaller numeral is at the right of the bigger one.

Here comes the math!

IV + II = VI & VI - II = IV

IX + II = XI & XI - II = IX

XL + XX = LX & LX - XX = XL

XC + XX = CX & CX - XX = XC

CD + CC = DC & DC - CC = CD

CM + CC = MC & MC - CC = CM

What about Roman numerals for numbers greater than or equal to 4,000? There's another Web page on the Math Trick Menu with more information. See "Why Numbers Are Important".