Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

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Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

Behaviors

Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

Networks

Search

Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Kings And Aces

You are given 4 aces and 4 kings from the standard deck of 52 cards as (above diagram). How many different pairs of cards, each pair consisting of one ace and one king, can you form from the aces and the kings?

**The string**: S_{7}P_{6}A_{64} (Multi-criteria - permutation);
**The Math**:

Pj Problem of Interest (PPI) is of type *Grouping/Interaction*.

Let us assign numbers to the identities of the aces and kings. In other words:

Let the king of diamond be 1, king of heart be 2, king of spade be 3 and king of club be 4.

Also let the ace of diamond be 5, ace of heart be 6, ace of spade be 7 and ace of club be 8.

Then the pairing are as follows:
15, 16, 17, 18, 25, 26, 27, 28, 35, 36, 37, 38, 45, 46, 47, 48.

Therefore there are 16 different ways to pair the aces and the kings given the constraint.

In general, given *n* groups, each of size *m*, the number of groups that can be formed such that each of the formed groups contains one member from each of the *n* groups, is *m ^{n}. Using this expression for the current problem, we have 4^{2} = 16.
*

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Single Variable Functions

Conics

Ordinary Differential Equations (ODEs)

Vector Spaces

Real Numbers

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings