Mathscapes

Solving Problems with Mathematical Landsapes

Start| 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th | 10th | 11th | 12th | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | SFO | LAX | LAS | PHX | SEA | DEN | DFW | IAH | ORD | CTL | ATL | MIA | JFK | SEA | SFO | LAS | LAX | DEN | PHX | DFW | ORD | IAH | CLT | ATL | JFK | MIA | LAX | LAS | SFO | PHX | DEN | SEA | DFW | IAH | ORD | CLT | ATL | MIA | JFK | LAS | LAX | PHX | SFO | DEN | SEA | DFW | IAH | ORD | CLT | ATL | MIA | JFK | PHX | LAS | LAX | SFO | DFW | DEN | IAH | SEA | ORD | CLT | ATL | MIA | JFK | DEN | PHX | LAS | DFW | LAX | ORD | IAH | SFO | SEA | CLT | ATL | JFK | MIA | DFW | IAH | DEN | CLT | ORD | PHX | ATL | LAS | MIA | LAX | JFK | SFO | SEA | IAH | DFW | CLT | DEN | ATL | PHX | MIA | ORD | LAS | LAX | JFK | SFO | SEA | ORD | CLT | ATL | JFK | DFW | DEN | IAH | MIA | PHX | LAS | SEA | LAX | SFO | CLT | ATL | MIA | ORD | DFW | IAH | JFK | DEN | PHX | LAS | LAX | SFO | SEA | ATL | CLT | JFK | ORD | MIA | DFW | IAH | DEN | PHX | LAS | LAX | SFO | SEA | MIA | CLT | ATL | IAH | DFW | JFK | ORD | DEN | PHX | LAS | LAX | SFO | SEA | JFK | ATL | ORD | CLT | MIA | DFW | IAH | DEN | PHX | LAS | SEA | LAX | SFO |

Step 2

Here	to	There	Position
DEN	-->	DFW	3rd
DFW	-->	DEN	2nd

Multiply the positions together.

| | | | --- | --- | --- | --- | DEN | <-> | DFW | 6 |

Full Table

City	SFO	SEA	LAX	LAS	PHX	DEN	DFW	IAH	ORD	CLT	ATL	MIA	JFK
SFO	---	4	2	6	9	35	66	77	96	99	110	121	144
SEA	4	---	15	10	35	32	72	96	70	108	120	144	110
LAX	2	15	---	1	3	16	54	63	88	90	100	110	132
LAS	6	10	1	---	2	8	42	56	72	81	90	99	108
PHX	9	35	3	2	---	5	20	30	64	72	80	88	96
DEN	35	32	16	8	5	---	6	18	25	63	70	84	77
DFW	66	72	54	42	20	6	---	1	16	12	30	32	50
IAH	77	96	63	56	30	18	1	---	42	10	24	18	60
ORD	96	70	88	72	64	25	16	42	---	3	6	42	6
CLT	99	108	90	81	72	63	12	10	3	---	1	2	18
ATL	110	120	100	90	80	70	30	24	6	1	---	8	2
MIA	121	144	110	99	88	84	32	18	42	2	8	---	20
JFK	144	110	132	108	96	77	50	60	6	18	2	20	---

Step 3 Order the Cites

This is the "Landscape" you now traverse.

Next	SFO	SEA	LAX	LAS	PHX	DEN	DFW	IAH	ORD	CLT	ATL	MIA	JFK
1st	LAX	SFO	LAS	LAX	LAS	PHX	IAH	DFW	CLT	ATL	CLT	CLT	ATL
2nd	SEA	LAS	SFO	PHX	LAX	DFW	DEN	CLT	JFK	MIA	JFK	ATL	ORD
3rd	LAS	LAX	PHX	SFO	DEN	LAS	CLT	MIA	ATL	ORD	ORD	IAH	CLT
4th	PHX	DEN	SEA	DEN	SFO	LAX	ORD	DEN	DFW	IAH	MIA	JFK	MIA
5th	DEN	PHX	DEN	SEA	DFW	IAH	PHX	ATL	DEN	DFW	IAH	DFW	DFW
6th	DFW	ORD	DFW	DFW	IAH	ORD	ATL	PHX	MIA	JFK	DFW	ORD	IAH
7th	IAH	DFW	IAH	IAH	SEA	SEA	MIA	ORD	IAH	DEN	DEN	DEN	DEN
8th	ORD	IAH	ORD	ORD	ORD	SFO	LAS	LAS	PHX	PHX	PHX	PHX	PHX
9th	CLT	CLT	CLT	CLT	CLT	CLT	JFK	JFK	SEA	LAS	LAS	LAS	LAS
10th	ATL	JFK	ATL	ATl	ATL	ATL	LAX	LAX	LAS	LAX	LAX	LAX	SEA
11th	MIA	ATL	MIA	MIA	MIA	JFK	SFO	SFO	LAX	SFO	SFO	SFO	LAX
12th	JFK	MIA	JFK	JFK	JFK	MIA	SEA	SEA	SFO	SEA	SEA	SEA	SFO