October 2010
Problem of the Month

Scrabble Problem

A game of Scrabble was played by two mathematics students, and peculiarly enough, every word was a math word (or almost!).

The game was played on a regulation Scrabble board using the standard rules for Scrabble.   The following abbreviations are used on the board: TWS = Triple Word Score; DWS = Double Word Score; TLS = Triple Letter Score; and DLS = Double Letter Score. The chart below gives the frequency and the value of the letter tiles:

Tile	Freq.	Value		Tile	Freq.	Value
A	9	1		N	6	1
B	2	3		O	8	1
C	2	3		P	2	3
D	4	2		Q	1	10
E	12	1		R	6	1
F	2	4		S	4	1
G	3	2		T	6	1
H	2	4		U	4	1
I	9	1		V	2	4
J	1	8		W	2	4
K	1	5		X	1	8
L	4	1		Y	2	4
M	2	3		Z	1	10
				blank	2	0

Play alternated between the two math students until all but three tiles were played (V, F, and U).   You must determine each word played, correct placement on the board, and the score at the end of the game.   You are given a clue for each word played.   The correct placement of the first letter of the first word has been given to you.   Remember that no more than SEVEN additional letters may be placed at one time.   In this game, blanks were played only after all tiles of a particular letter were played (the two blanks were played in move #13 and move #17).

Fill in the score in the chart below:

Score		Clues
Player 1	Player 2
_____	X	1. The name of the point whose coordinates are (0,0).   Word begins at (6,8).
X	_____	2. One of the three undefined terms of geometry (a "dot" with zero dimensions).   Word begins at (11,11).
_____	X	3. The name for the y-coordinate.   Word begins at (6,8).
X	_____	4. The equation y = 3x - 1 is called a _______ equation.   Word begins at (5,5).
_____	X	5. The line, all of whose y-coordinates equal zero, is called the x-______. Word begins at (6,3).
X	_____	6. An angle divides the plane into three sets of points: the angle, the exterior, and the _______.   Word begins at (8,8).
_____	X	7. The formula is called the ______ formula. Word begins at (11,14).
X	_____	8. The mathematical theory, founded by John von Neuman, of optimal behavior in situations involving conflicts is called _____ theory.   Word begins at (9,14).
_____	X	9. One of the four sections into which the two coordinate axes separate the plane. Word begins at (8,12).
X	_____	10. The first number of an ordered pair is called the x-_____ .  Word begins at (6,10).
_____	X	11. is the formula for the _____ .   Word begins at (9,10).
X	_____	12. Plural of locus.   Word begins at (4, 10).
_____	X	13. The identity element for addition.   Word begins at (5,13).
X	_____	14. Plane geometry is _____ - dimensional.   Word begins at (11,7).
_____	X	15. A statement that is proven to be true.   Word begins at (4,1).
X	_____	16. is known as the _____ formula.   Word begins at (15,15).
_____	X	17. An arc of more than 180 degrees is called a ______ arc.   Word begins at (2,7).
X	_____	18. An angle whose measure lies between 90 and 180 degrees is called ______ .   Word begins at (13,7).
_____	X	19. The integer that follows four.   Word begins at (2,12).
X	_____	20. The segment opposite the vertex angle of an isosceles triangle.   Word begins at (11,3).
_____	X	21. In BASIC computer language, this statement assigns a value to a variable.   Word begins at (4,3).
X	_____	22. A type of function.   Word begins at (3,14).
_____	X	23. In ballistics, the angle between the direction of the axis of a shell and the   direction of its velocity vector is the _____ angle.   Word begins at (3,8).
X	_____	24. Owed or owing as a debt.   Word begins at (2,2).
_____	X	25. One of the most important items in life insurance is the person's _____.   Word begins at (13,12).
X	_____	26. "Every positive integer greater than 1 is prime or can be expressed as a product of prime numbers"   is called _____ Fundamental Theorem of Arithmetic.   Word begins at (13,5).
_____	X	27. These two students always _____ about math.   Word begins at (1,14).
X	_____	28. Player 2 was left with the letter tiles F, U, and V, which she could not use.
_____	_____	TOTAL SCORE

---

Solution to the Problem:

Player #1			Player #2
Points	Word	Move	Points	Word
14	origin	1
		2	14	point
15	ordinate	3
		4	12	linear
20	axis	5
		6	27	interior
13	midpoint	7
		8	9	game
58	quadrant	9
		10	19	coordinate
9	slope	11
		12	6	loci
24	zero	13
		14	7	two
13	theorem	15
		16	99	distance **
12	major	17
		18	16	obtuse
20	five	19
		20	6	base
3	let	21
		22	14	kei
9	yaw	23
		24	8	due
4	age	25
		26	6	the
20	yak	27
		28	-9	-----
_____	_____	_____	_____	_____
234		TOTAL	234

** The word DISTANCE occupies two triple word scores.
  The rules state that the value for the word is tripled and then tripled again.

Correctly solved by:

No one

Send any comments or questions to: David Pleacher