Modular Arithmetic (SchoolTube)
What is Modular Arithmetic?
Modular Arithmetic expresses the
relationship between a number, its quotient, and its remainder.
Example Modular Arithmetic
If it is 2:00, and I have to be
somewhere in 3 hours, when do I need to be there? 5:00.
If it is 8:00 and I need to be somewhere in 4 hours, when
do I need to be there? 12:00. What if it is 10:00 and I need
to be somewhere in 4 hours? I need to be there at 2:00, not
14:00. Why? It is because we “reset” our clocks at 12.
This is modular arithmetic!
Modular Arithmetic Formula
Modular Arithmetic in Card Games
Magicians (or those aspiring to be) will
place cards purposefully to keep them in the same modular position.
For example, in (mod 4), 0, 4, 8, 12, etc are all the same! So, in a
card trick, a magician would keep a card they need in the “zero”
position in either the 0, 4, 8, or 12 (etc) location.
Combinatorics (Owlcation)
What is Combintorics?
Combinatorics is the concept
of seeing how many combinations there can be, in this
case specifically when order does not matter
Example Combinatorics
A person has four cards and wants
to know how many ways they can choose two of them (4 choose 2).
Let us say those cards are labeled A, B, C, and D. Then, a person
could choose AB, AC, AD, BC, BD, or CD (6 combinations). Thus, we
would say that 4 choose 2 equals 6
Combinatorics Formula
Combinatorics in Card Games
Combinations are used with card games
to see the probability that a card will be drawn or placed