mathamitions help

[Oscar Lopez]

mathamitions help

use clues a thru h to solve puzzle

a) I am a rectangle

b) my dimensions are consecutive counting numbers

c) my perimeter (the total number of linear units around me) has 4 factor

d) the sum of my length and width is a prime number

e) one of my dimensions is an odd number and one is even

f) my area is not a square number

g) my perimeter is 3 less then a prime number and 1 more then another prime number

h) my area is less then the 10th square number and greater than the 7th prime number

draw a picture of me and label my dimensions, area, and perimeter

any help I can get to solve this out is a big help

 

[Raser x]

is it a 3 x 4 rectangle?

consecutive counting numbers 3,4

3+3+4+4 =12 is factorable by 4

length plus width =7 is prime

demension 3 is odd, 4 is even

12 is not a square number 3x3=9 , 4x4=16

perim is 14 next prime is 17, three more than 14. 13 is one prime before 14

the tenth square number is 100. the seventh prime number is 13.............I think. hope.guess

:wacko:

 

[David Johnson 2]

This seems easy enough, but something isn't adding up right.

Call the width x and the length y.

Using Clue H, you get 17 < x*y < 100.

Now according to Clue B, x and y are consecutive counting numbers such as 1 and 2, 2 and 3, 3 and 4, etc. Using this information along with Clue H, the only available groups of x and y are (4,5), (5,6), (6,7), (7,8), (8,9), (9,10).

Now using Clue D, you can eliminate (4,5) and (7,8). Thus leaving (5,6), (6,7), (8,9), (9,10).

Now using Clue G, the only group of numbers that satisfies the parameters are 9 and 10.



So my answer would be 9 and 10 for the length and width.



However what doesn't make sense is Clue C. I do not believe that it is possible to have a rectangle with dimensions of 2 consecutive counting numbers, that fits this clue. Here is a short mathematical proof.

Perimeter = 2x + 2y.

If Perimeter has a factor of 4, then (2x + 2y)/4 is an integer.

Thus (x + y)/2 is an integer.

Any integer that is divisible by 2 is EVEN (by definition of even numbers).

Since the numbers are consecutive counting numbers then one number must be odd and the other even (and Clue E points this out).

However the sum of an even and an odd number is ALWAYS and ODD. Thus this clue can never be valid.



Are you sure you have Clue C written correctly?

 

[David Johnson 2]

RaserX...

Just a note 3+3+4+4 =14 which is NOT factorable by 4

Nice try though.

 

[Greg Hatch]

a. your rectangle is 9 x 10

b. which are consecutive counting numbers

c. your perimeter ( 9 + 9 +10 + 10 = 38) is evenly divisibe by 1,2,19, and 38

d. 9 + 10 = 19 ---> which is prime

e. 9 is odd, 10 is even

f. area = 9 x 10 = 90 ---> not a square number

g. perimeter 38: 3 less than a prime number ---> 41 is prime: 1 more than another prime ---> 37

is prime

h. area is 9 x 10 = 90 which is less than 10th square number (which is 100)

prime numbers = 2 3 5 7 11 13 17 19 23 29

31 37 41 43 47 53 59 61 67 71

73 79 83 89 97 101 103 107 109 113

127 131 137 139 149 151 157 163 167 173

and definitely greater than the 7th prime which is 17

 

[Greg Hatch]

I took clue c to mean that the perimeter has 4 factors, not that 4 is a factor



Figured that an s was left off



The one that got me was why give the area such a large range 17 < area < 100

 

[David Johnson 2]

ST-Miner got it...

Clue C should read "4 factors" not "4 factor". I thought you meant had 4 as a factor (meaning divisible by 4). It's amazing what 1 letter can do to a problem.



The correct answe definitely has to be 9x10.



PS - I am not sure what Mathamitions are, but Mathematicians are the people you were looking for.

 

[Bill V]

oscar--Forget a mathematician. You need someone to help with spelling first.



(Just kidding.)

 

[Mike Wilson]

Answer: Ohio...



Next Question.

 

[Oscar Lopez]

thanks for your help everyone. you are all the best

 

[Raser x]

O'well math wasn't my strong suit...But thanks guys. I did more math last night than I have in a loooong time. even it it wasn't right. :huh: