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A pond in a garden 2020-04-09
From Jin:
c) I have a large square pond set inside a square garden: both the pond and the garden have sides which are a whole number of metres, and outside the pond, the garden is grassed over. The area covered by grass is 188 square metres. Find the area of the pond. (5 marks)
Answered by Penny Nom.
How many cubes are in a 3x3x3 cube? 2019-06-24
From Darren:
Dear Sir/Madam, How many cubes of different sizes (eg. 1x1x1, 2x2x2, 3x3x3) are there in total in say, a 3x3x3 cube? I have trouble figuring this out.

Yours faithfully,

Answered by Penny Nom.
Subdividing a rectangle into squares 2018-05-13
From jeverzyck:
A rectangular board is 108cm wide and 156 cm long Equal squares as large as possible are ruled off this board.Find the size of the square.How many squares are there?
Answered by Penny Nom.
Expand (5x-9)(5x+9) 2018-03-01
From adil:
expand the following:

Answered by Penny Nom.
A question about perfect squares 2018-02-04
From Jolyn:
Find the smallest possible value of a whole number m if 648x m is a perfect square
Answered by Penny Nom.
Squares and rectangles 2017-07-15
From Tront:
So, there's a general rule that all squares are rectangles but not all rectangles are squares. Im trying to find a term that would describe this relationship. I've found that if all of A is B but not all B is A then I'd say that A is a subset of B, but is there a term that describes the relationship as a whole? I don't want to describe the components, I want to describe the relationship as a whole.
Answered by Penny Nom.
1/1-cosine(2x) - 1/1+ cos(2x) 2016-12-14
From Sean:
1/1-cosine(2x) - 1/1+ cos(2x)
Answered by Penny Nom.
x^2 = -16 2016-12-12
From A student:
x to the second power = -16

what number solves the equation?

Answered by Penny Nom.
2^48 - 1 2015-06-13
From Soham:
The number 2^48-1 is divisible by two numbers between 60 and 70. The sum of the two numbers is?
Answered by Penny Nom.
An 8 pointed star inscribed in a circle 2015-04-10
From Kermit:
How do you find the area of the star that is formed by two squares and surrounded by a circle. The only given information is that the radius of the circle is 10.
Answered by Penny Nom.
(x-3)^2-(x+3)^2 2014-11-13
From Bernice:
Answered by Penny Nom.
Can 100r^2-81z^2 be factored? 2013-12-08
From Rosa:
Can 100r^2-81z^2 be factored?
Answered by Penny Nom.
Squares and cubes 2013-08-02
From Sandra:
What whole number equals 25 when it is squared and 125 when it is cubed?
Answered by Penny Nom.
(4- 4cos^4 x)/(sin^2 x) 2013-05-18
From Agnes:
How I can solve this question :

Simplify (4- 4cos^4 x)/(sin^2 x) and write in terms of sin x

Answered by Penny Nom.
Difference of squares 2012-11-19
From Qelibar:
Please factorise x^2y^2 - 4
Answered by Penny Nom.
Two equations involving fractions 2012-06-12
From Fatima:
Hi ,teacher gave two question to my daughter as follows
Solve 2/x+3=(1/xx-9)-(1/x-3)and
Solve (4/x-2)-(x/x+2)=16/xx-4

Please help me
Thanks & regards fatima

Answered by Penny Nom.
Sum and difference of squares 2011-12-31
From Anne:
Se x e y são números reais distintos, então:
a) (x^2 + y^2) / (x - y) = x + y
b) (x^2 + y^2) / (x - y) = x - y
c) (x^2 - y^2) / (x - y) = x + y
d) (x^2 - y^2) / (x - y) = x - y
e) Nenhuma das alternativas anteriores é verdadeira.

Answered by Harley Weston.
Squares and triangles 2011-12-06
From Liaqath:
You have squares and triangles.
Altogether there are 33 sides.
How many squares do you have?
How many triangles do you have?

Answered by Penny Nom.
U(n+1) = 2Un + 1 2011-05-22
From Cillian:
In a certain sequence, to get from one term to the other you multiply by 2 and add 1, i.e. This is a difference equation of form: U(n+1) = 2Un + 1. prove that there is a maximum of 2 perfect squares in this sequence
Answered by Claude Tardif.
Two whole numbers 2011-05-11
From yolanda:
The sum of two whole numbers is 12.If the sum of the squares of those numbers is 74,what are the two numbers?
Answered by Penny Nom.
(3x+4y)^2 - (2x-y)^2 2011-03-16
From Taiwo:
pls could some one help me with this question? thanks as lot

(3x+4y)^2 - (2x-y)^2

Answered by Penny Nom.
Two problems 2010-04-13
From Dorothy:
1. Explain why the number 123, 456, 789, 101, 112 cannot be a perfect square. (Hint: What is the units digit?)

2. A substance doubles in volume every minute. At 9:00A.M., a small amount is placed in a container. At 10:00A.M., the container is just full. At what time was the container one-eighth full?

Answered by Robert Dawson.
Is it a square? 2010-01-29
From Manick:
I have a question. how to find whether a given integer is a perfect square or not?
Answered by Robert Dawson.
(9 - x^2)/(x - 3) 2009-12-04
From Sandy:
I need to know how to solve this.

Answered by Penny Nom.
Cubes and squares 2009-09-16
From Stanley:
What is a three consecutive digit number like 5,6,7 , which is two less than a cube and two more than a square?
Answered by Robert Dawson.
The units digit is 5 2009-02-02
From Ray:
the number that when squared the units digit is 5
Answered by Penny Nom.
Factor x^2 - y^2 2009-01-20
From Shell:
complete Factor: x^2-y^2
Answered by Penny Nom.
Factoring 2008-11-19
From Neji:
How do you factor (y-z) (y+z) (y^4+y^2z^2+z^4) and get (y+z)(y^2-yz+z^2) (y-z) (y^2+yz+z^2) as the answer?
Answered by Harley Weston.
z(z+1)-x(x+1) / z-x 2008-09-30
From sylvia:
z(z+1)-x(x+1) / z-x


Answered by Penny Nom.
a(a+1) - b(b+1) 2008-09-30
From Shaun:
I need to factor (a-b) out of the following: a(a+1) - b(b+1). I know it is simple but I cannot remember how.
Answered by Penny Nom.
Simplifying Algebraic Expressions 2008-08-22
From Jacky:
Answered by Penny Nom.
Factoring x^2 + 729 2008-08-19
From peter:
hello I,am having trouble factorising a polynomial into polynomial factors with real coefficients please can you help the polynomial is x^2+729
Answered by Harley Weston.
The sum of the squares of the fibonacci numbers 2008-04-27
From Thomas:
Hey I have a question for a research topic that our teacher set us, It is regarding the sum of the squares of the fibonacci numbers.

The question says describe the pattern that exists and write a general formula that describes the relationship illustrated above. I can see the pattern that is occurring but i cannot put this into a general formula. Any help would be appreciated. Thanks Tom

Answered by Victoria West.
10 squares drawn one inside another 2008-02-25
From Rajesh:
There are 10 squares drawn one inside another.The diagonal of the inneremost square is 20 units. if the distance b/w the corresponding corners of any two successive squares is 1 unit, find the diffrence between the areas of the eigth and seventh square counting from the innermost
Answered by Stephen La Rocque.
5x^2 - 45 2008-02-11
From Tiana:
factor: 5x^2 - 45
Answered by Stephen La Rocque.
Expand (a^4 - b^4) 2007-11-17
From Saif:
how would you expand (a^4 - b^4) ???
Answered by Stephen La Rocque and Victoria West.
A 5 by 5 checkerboard 2007-09-17
From Darren:
Hi, I'm Darren and i have some questions to ask you about this problem: In a 5 by 5 checkerboard : how many 2 by 2 squares are there, what other sizes of squares do you need to count and how many of of each size of squares can you find; how many squares did you find in all
Answered by Victoria West.
Two squares 2007-08-18
From Jerry:
The vertex E of a square EFGH is inside a square ABCD. The vertices F, G and H are outside the square ABCD. The side EF meets the side CD at X and the side EH meets the side AD at Y. If EX = EY, prove that E lies on BD.
Answered by Chris Fisher.
Find all numbers which are both squares and cubes 2007-07-30
From Arul:
what is the easiest way to find the number which is both a square and a cube? the numbers i know are 64 and 729 which is both a sqr and a cube. i took long time to solve this.. is there any easier way?
Answered by Steve La Rocque.
Simplifying an algebraic fraction expression 2007-07-25
From Jessica:
How do I simplify b/(b2-25) + 5/(b+5) - 6/b?
Answered by Stephen La Rocque.
Simplifying complex denominators 2007-06-21
From Krys:
How do I simplify completely? ((4+i ) / (3+i )) - ((2-i ) / (5-i ))
Answered by Stephen La Rocque.
Counting squares 2007-05-12
From Bridget:
Explain how many squares there are on a board measuring 4 by 4 units,
Answered by Stephen La Rocque and Penny Nom.
Using the "difference of squares" formula how do I compute 27 * 33? 2007-04-02
From Sarah:
Using the "difference of squares" formula how do I compute 27 * 33?
Answered by Penny Nom.
Factoring polynomials 2007-02-14
From Joe:
I am in the eighth grade, and we are learning the equivalent of Algebra 2. I have no ides how to factor (x-2)(x^2-1)-6x-6 You help is most aprreciated. Thank you! Joe
Answered by Stephen La Rocque.
How many squares are there on a checkerboard 2006-12-17
From Tania:
how many squares are there altogether on the checkerboard (including the 64 small squares)?
Answered by Penny Nom.
Factoring m^4-9^n 2006-12-07
From Josh:
I can not figure out how to completely factor m^4-9^n.
Answered by Penny Nom.
1X2X3X4+1=5^5 2006-11-23
From Liza:
1X2X3X4+1=5 square
2x3x4x5+1=11 square
What is the rule for this?

Answered by Stephen La Rocque and Penny Nom.
What's 3x squared? 2006-11-02
From Cath:
What's 3x squared?
Answered by Penny Nom.
Squaring numbers 2006-10-08
From Timothy:
did anyone ever try to teach that the easiest way to find the next square in a group of numbers is to add the next odd number in the sequence. for example: 1 squared is 1, 2 squared is 4,difference of 3.the next odd number is 5 so the next square would be 4 +5 or 9
Answered by Paul Betts and Penny Nom.
A square palindrome 2006-09-11
From Liz:
What is the least three-digit palindrome that is a square number?
Answered by Stephen La Rocque.
Two squares 2006-03-25
From Debbie:
A small square is constructed. Then a new square is made by increasing each side by 2 meters. The perimeter of the new square is 3 meters shorter than 5 times the length of one side of the original square. Find the dimension of the original square
Answered by Stephen La Rocque.
Find the nth term 2005-12-14
From Kevin:
How do i find the nth term of 1 4 9 16 25 36
Answered by Penny Nom.
The perimeter of a collection of squares 2005-12-11
From Catherine:
using 12 squares, make a number of patterns (squares joined). Find the perimeters. Find out how many points in the shape have four radiating lines i.e. are two lines intersecting. Write an equation to state the relationship between the lines and the perimeter.
Answered by Penny Nom.
Tables with perfect squares 2005-11-30
From Craig:
A table consists of eleven columns. Reading across the first row of the table we find the numbers 1991, 1992, 1993,..., 2000, 2001. In the other rows, each entry in the table is 13 greater than the entry above it, and the table continues indefinitely. If a vertical column is chosen at random, then the probability of that column containing a perfect square is:
Answered by Claude Tardif.
A block pyramid 2005-11-05
From Kyle:
if i make a block pyramid and it puts a new perimeter around it every time, for example the first layer will be 1 block across (area=1), the second layer will be 3 blocks across (area=9), the third layer will be 5 blocks across (area=15),etc. The normal block pyramid. I have figured out that in order to figure out the number of blocks needed for a certain level, the equation is (2x-1)2 or (2x-1)(2x-1), where x is equal to the level. For example, on the fourth level, the equation tells you that it will have an area of 49. How would i make an equation for the total number of blocks up to the level. For example, in order to complete 1 level you need 1 block, for 2 levels you need 10 blocks, for three levels you need 35 blocks, and for 4 levels you need 84 blocks.
Answered by Penny Nom.
An odd number of factors 2005-10-06
From Ramneek:
What is the common name used for numbers that have an odd number of factors?
Answered by Claude Tardif.
1,4,9,1,6,2,5,3,6,4,9,6,4,8,1 2005-08-30
From Liz:
Find the next four numbers to the sequence 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,___,___,___,___.
Answered by Penny Nom.
Explain why 3(x+2) = 3x+2 is incorrect 2005-03-28
From Cynthia:
An algebra student incorrectly used the distributive property and wrote 3(x+2) = 3x+2. How would you explain to him the correct result, without the use of the distributive law?

Explain why the square of the sum of two numbers is different from the sum of the squares of two numbers.

Answered by Penny Nom.
What is the least three-digit palindrome that is a square number? 2005-02-12
From Ben:
What is the least three-digit palindrome that is a square number?
Answered by Chris Fisher and Penny Nom.
Is a square a rectangle? 2004-11-21
From Carol:
I am a teacher. In an FCAT sixth grade review test, there was a question to the students to draw a square and then they referred to it as a rectangle.

What is the definition that makes a rectangle a square that can be taught to the students without confusing them.

Answered by Walter Whiteley.
Factoring 2004-07-19
From A student:
Factor completely:
3x3 - 24y3
54x6 + 16y3
16xy - 4x - 4y - 1
0.09x2 - 0.16y2

Answered by Penny Nom.
3x squared - 27 / x + 3 2004-05-04
From Stef:
3x squared - 27 / x + 3
Answered by Penny Nom.
Some factoring problems 2004-04-15
From KJ:

Factor these:
x3+125 -----> (x+5)3
8x3-27 -----> (?)
x2+36 -----> (x+6)2
x4-5x2+4 --> (?)

Answered by Penny Nom.
400, 100 and 2500 2003-12-21
From A student:
A person likes 400 but dislikes 300
He also likes l00 but dislikes 99
He also likes 2500 but dislikes 2400

Which of the following does John like
900, 1000, 1100 or 2400

Answered by Penny Nom.
Difference of squares 2003-11-24
From Susie:

Factor assuming that n is a positive #

Problem: (I will give it to you in words beacuse I don't know how to do exponents on the computer.) Forty-five r to the 2n power minus five s to the 4n power. I was hoping you could walk me through it not just give me the answer.

Answered by Penny Nom.
A least squares line 2003-11-09
From Michelle:
Hooke's Law asserts that the magnitude of the force required to hold a spring is a linear function of the extension e of the spring. That is, f = e0 + ke where k and e0 are constants depending only on the spring. The following data was collected for a spring;

e: 9 , 11 , 12 , 16 , 19
f : 33 , 38 , 43 , 54 , 61

FIND the least square line f= B0 + B1x approximating this data and use it to approximate k.
Answered by Penny Nom.

Squares in a rectangle 2003-10-21
From Raj:

Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle.

If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares.

Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle.

Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle?

Answered by Chris Fisher.
Numbers John likes 2003-06-20
From Steve:
John likes 400 but not 300; he likes 100 but not 99; he likes 2500 but not 2400.

Which does he like?

Answered by Penny Nom.
The square of my age was the same as the year 2003-04-14
From Pat:
Augustus de Morgan wrote in 1864, "At some point in my life, the square of my age was the same as the year." When was he born?
Answered by Penny Nom.
Can twice a square be a square? 2003-03-25
From Mike:
The other day it occurred to some students that they could think of no square number which is an integer, which can be divided into two equal square numbers which are intergers, Or put another way, no squared integer when doubled can equal another square integer. For example 5 squared plus 5 squared is 50, but 50 is not a square number.
Answered by Walter Whiteley and Claude Tardif.
Can a square be considered a rectangle? 2003-02-27
From Carla:

Can a square be considered a rectangle? (since opposite sides are same length and parallel)

Would a regular hexagon or octagon be considered a parallelogram since its opposite sides are parallel? or does a parallelogram HAVE to have only 4 sides?

Answered by Penny Nom.
Factoring 2002-12-11
From Larry:

how do u factor trinonmials

EX: X 3 + Y 3

X 3 - 8Y 3

8X 2 - 72

64A 3 - 125B 6

Answered by Penny Nom.
8 squares from 12 sticks 2002-10-08
From A student:
If you have 12 sticks the same size, how do you make them into 8 squares?
Answered by Claude Tardif.
A square of tiles 2002-08-30
From Rosa:
How do I go about finding a formula for the number of tiles I would need to add to an arbitrary square to get to the next sized square?
Answered by Penny Nom.
When is 1! + 2! + 3! + ... + x! a square? 2002-08-19
From Sarathy:
Solve :

1! + 2! + 3! + ... + x! = y 2

How do i find the solutions ?

Answered by Claude tardif.
A sequence 2002-01-16
From Chris:
I have spent two days trying to determine the pattern to the following set of numbers: 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,____. I need the next four numbers to the sequence.
Answered by Claude Tardif.
Linear regression 2002-01-16
From Murray:
If you have a set of coordinates (x[1],y[1]),(x[2],y[2]),...,(x[n],y[n]),find the value of m and b for which SIGMA[from 1 to m=n]AbsoluteValue(y[m]-m*x[m]-b) is at its absolute minimum.
Answered by Harley Weston.
Magic squares 2001-11-17
From A student:
7th grader wanting to find solution to magic square:

place the integers from -5 to +10 in the magic square so that the total of each row, column, and diagonal is 10. The magic square is 4 squares x 4 squares.

Answered by Penny Nom.
Squares of negative numbers 2001-11-03
From Susana:
I wanted to know if I can square a negative number..?
Answered by Leeanne Boehm.
Some algebra 2001-10-15
From James:
I cannot figure these out I was wondering if you could help me? I have no one to answer my questions.
  1. (7x2 – 3yz)2 – (7x2 + 3yz)2

  2. Use Pascal’s triangle to expand (2x – y)4

  3. 8x3 y - x3 y4

  4. (m + 3n)2 – 144

  5. 12x4 y – 16x3 y2 – 60x2 y3

  6. p3 q2 – 9p3 + 27q2 – 243

Answered by Peny Nom.
Squares of one digit numbers 2001-10-15
From Needa:
What two two-digit numbers are each equal to their right-most digit squared?
Answered by Penny Nom.
Pythagoras & magic squares 2001-10-09
From John:
My grandson became intrigued when he recently 'did' Pythagoras at elementary school. He was particularly interested in the 3-4-5 triangle, and the fact that his teacher told him there was also a 5-12-13 triangle, i.e. both right-angled triangles with whole numbers for all three sides. He noticed that the shortest sides in the two triangles were consecutive odd numbers, 3 & 5, and he asked me if other right angled triangles existed, perhaps 'built' on 7, 9, 11 and so on.

I didn't know where to start on this, but, after trying all sorts of ideas, we discovered that the centre number in a 3-order 'magic square' was 5, i.e. (1+9)/2, and that 4 was 'one less'. Since the centre number in a 5-order 'magic square' was 13 and that 12 was 'one less' he reckoned that he should test whether a 7-order square would also generate a right-angled triangle for him. He found that 7-24-25, arrived at by the above process, also worked! He tried a few more at random, and they all worked. He then asked me two questions I can't begin to answer ...

  1. Is there a right-angled triangle whose sides are whole numbers for every triangle whose shortest side is a whole odd number? and

  2. Is each triangle unique (or, as he put it, can you only have one whole-number-sided right-angled triangle for each triangle whose shortest side is an odd number)?

Answered by Chris Fisher.
Squares of Fibonacci numbers 2001-04-24
From Vandan:
What discoveries can be made about the sum of squares of Fibonacci's Sequence?
Answered by Penny Nom.
Squares on a chess board 2001-04-11
From Tom:
It was once claimed that there are 204 squares on an ordinary chessboard (8sq. x 8sq.) Can you justify this claim? "PLEASE" include pictures.

How many rectangles are there on an ordinary chessboard? (8sq. x 8sq.) "PLEASE" include pictures.

Answered by Penny Nom.
Difference of Squares 2001-02-22
From Bruno-Pierre:
I noticed the other day that if you substract two consecutive squared positive numbers, you end up with the same result as if you add up the two numbers.

Ex. 5 and 6 (2 consecutive positive numbers)
52 = 25
62 = 36
36 - 25 = 11 (Substraction of the squared numbers)
5 + 6 = 11 (Sum of the numbers)

A more algebric view:
a2 - b2 = a + b where a and b are consecutive positive positive numbers. (b = a + 1)

I wondered if this rule had a name, and who discovered it.

Answered by Penny Nom.
Difference of squares 2001-02-20
From Janna:
Hi! I was just wondering how you would factor x2 - 9y2.
Answered by Harley Weston.
Factoring (u-v)3+v-u 2000-12-15
From A parent:
I am a middle school teacher and a parent. I am snowed in and trying to help my 9th grader get ready for 9 weeks exams. I have tried to factor this problem to no avail. (u-v)^3+v-u. I have the answer but I need to know how it is done.
Answered by Penny Nom.
The sum of the cubes is the square of the sum 2000-10-10
From Otoniel:
Without using mathematical induction, or any other method discovered after 1010 a.d. , prove that the sum of i3, (where i, is the index of summation) from one to, n, is equal to ((n*(n+1))/2)2
Answered by Penny Nom.
n3 + 2n2 is a square 2000-09-04
From David Xiao:
determine the smallest positive integers, n , which satisfies the equation

n3 + 2n2 = b

where b is the square of an odd integer

Answered by Harley Weston.
The sum of the squares of 13 consecutive positive integers 2000-08-25
From Wallace:
Prove that it is not possible to have the sum of the squares of 13 consecutive positive integers be a square.
Answered by Harley Weston.
1+4+9+16+...n^2 = n(n+1)(2n+1)/6 2000-06-01
From Shamus O'Toole:
How do you derive that for the series 1+4+9+16+25.. that


Answered by Penny Nom.
Three factors 2000-02-21
From A parent:
Question from a parent helping a child, grade 4, with homework. Can a number have three factors? Name three numbers that have three factors.
Answered by Penny Nom.
Factoring ^6 2000-01-03
From Athena:

my name is Athena and I have a question on factoring: how would you figure this out:

(x6-y6) and (x6+y6)

Answered by Penny Nom.
Ben's observation 1999-10-28
From Emily Nghiem and Ben Rose:
As a teacher at a school called Educere in Houston, I have a ninth-grade student who discovered the following shortcut last year as an eight-grader. What he noticed is that given any two consecutive integers (or n and n+1 for any rational number greater than or equal to 2), the difference between their squares was equal to the sum of the two numbers.

Answered by Chris Fisher and Penny Nom.
An odd number of factors 1999-10-22
From Melissa:
What is the common name used for numbers that have an odd number of factors? What is the least positive integer that has exactly 13 factors?
Answered by Penny Nom.
A sum of two squares 1999-10-08
From Marksmen:
what is the smallest whole number that can be written two ways as a sum of two different perfect squares? i.e.11squared plus 3 squared is 121+ 9=130 and7 squared + 9squared=49 +81= 130. Are there any smaller? I am stumped!
Answered by Claude Tardif.
A difference of squares problem. 1999-07-24
From Michael and Stephanie Bixler:
If you have the equation x= n2 - m2 (ie 40= 72-32= 49-9) x must = a positive number

1) which squared numbers work as n and m
2) how does it work
3) if my teacher gave me the number for x; how could I figure out this problem
Answered by Harley Weston.

Introductory Algebra 1999-05-19
From Pat:
(2 + sq. root of 3) x (2 - sq. root of 3) = 1

Please show me the work.
Answered by Harley Weston.

Factoring 1999-03-30
From Maggie Stephens:
I don't know anything about factoring would you plese help me.

3x4 - 48

54x6 + 16y3


12x2 - 36x + 27

9 - 81x2

a3 + b3c3

I would greatly appreciate any help you can give me thanks.
Answered by Jack LeSage.

Factoring 1999-03-08
From L. Sivad:

Answered by Penny Nom.
Magic Squares 1999-02-11
From Katie Powell:
My name is Katie Powell. I'm in the 7th grade, taking Algebra. I live in Houston, Texas. My problem is this:

"Use the numbers 1-9 to fill in the boxes so that you get the same sum when you add vertically, horizontally or diagonally."

The boxes are formed like a tic-tac-toe -- with 9 boxes -- 3 rows and 3 columns.

Can you help?
Answered by Jack LeSage.

Students and Lockers 1998-10-02
From Mike:
There is a row of 1000 lockers.
There is a line of 1000 students.

Student number 1 starts at the first locker and opens all 1000. Student number 2 starts at the second locker and closes every other one. Student number 3 starts at the third locker and goes to every third one, closing the open ones and opening the closed ones. Student number 4 does the same with every fourth locker and so on down the line... After all 1000 students have gone how many lockers are open and which ones are they?

Please help! There is proboly a simple solution but we couldnt figure it out for the life of us. Please let us know how you solve it.
Answered by Patrick Maidorn and Penny Nom.

Difference of squares 1998-06-23
From Kristen Smelsky:
Solve the following using a difference of squares:

4x(squared) minus 4xy plus y(squared) minus m(squared) plus 2m minus 1
Answered by Penny Nom.

x^2 = ...444 1998-02-23
From James Bauer:
What is the first interger that when squared ends in three 4's? (ex. x^2 = ...444)

Prove that there are no intergers that when squared end in four 4's (ex. x^2 = ...4444)
Answered by Penny Nom.

Why QUADratic? 1997-03-19
From Paula Miller:
A student today asked me why a quadratic, with highest power of degree 2, was called a QUADratic. We're awaiting the answer with baited breath! :)
Answered by Chris Fisher and Walter Whiteley.



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