







A pattern rule for a sequence 
20161028 

From Grace: Here's a Grade 7 question, we need to find the pattern rule:
1  1
2  3
3  6
4  10
......
It may involve exponents, but we can't seem to figure it out.
thank you.
Grace. Answered by Penny Nom. 





4 digit strings using the digits 1, 2, 3 and 4 
20150614 

From Gary: What is the number of possible combinations using the following fact pattern?
A. Each combination must have 4 numbers.
B. The possible numbers to choose from are 1, 2, 3, 4
C. The numbers can be included in the combination more than once. For example, it can be 1111.
Is it possible to generate a schedule of the possibilities? Answered by Penny Nom. 





A pattern for a truncated cone 
20131220 

From Josh: I need to know how to layout a truncated cone with a base diameter of 18" a top
Diameter 15.25 and a height of 20". Your help will be greatly appreciated. Answered by Penny Nom with a spreadsheet by Don. 





A lamp shade 
20120515 

From Fleur: I am helping my child make a cone lampshade, the measurements are as follows in "cm's"
21 cm = height
8 cm = top diametre
40 cm = bottom diametre
Please could you give the pattern (cut out) dimensions for final cut. Answered by Penny Nom. 





A question about a pattern 
20120402 

From Steven:
A 
B 
C 
D 
E 
F 
(G) 
1 
3 

100 
100 
33 
(67) 
D is divided by A and B to give E and F the difference between E and F is G
C is added to D to give the new D number.
3 
5 
120 
330 
110 
66 
(44) 
4 
6 
130 
460 
115 
77 
(38) 
5 
7 
140 
600 
120 
86 
(34) 
Following the pattern you might expect a massive increase in C to result in a significant decrease in G but...
6 
8 
1000 
1600 
267 
200 
(67) 
G actually increases and goes back to square 1 Why?
Answered by Robert Dawson. 





Building a tipi 
20120129 

From Lacy: Hi there!
We are building a tipi for our children. We want to build a large one about 15ft tall with a base of about 15 feet diameter. I am trying to figure out how much canvas we need to accomplish this. I graduated about 20 years ago and am struggling. Please help if you can. Answered by Penny Nom. 





A pattern for a cone 
20110830 

From Izzy: I need to create a cone as a prop and my math is not good enough to create the pattern.
Here are my instructions :
The diameter is 2'5" and it has to be 4 feet tall. It is a giant cone. I want it to be pointy at the end, not truncated. Answered by Penny Nom. 





The nth term 
20101122 

From Daphne:
Question from Daphne, a student:
Hi,
My name is Daphne and I am having trouble with a math problem. I am given this pattern below and asked to find an expression for the number of Bs in the nth term of the pattern. Someone please help!!!
ABBA
AABBBAA
AAABBBBAAA
AAAABBBBBAAAA
The next part asks me to find the ratio of Bs to total letters in the nth term.
Finally it says to use my expression to determine which term has exactly 35% Bs. Answered by Penny Nom. 





Finding a Number Pattern 
20100922 

From Cheryl: Sunshine Math  4, Jupiter 1, question 4 which is (a, b, c & d). I am wanting to know question 4d. Think about the following list of number pairs. Three is the first number of a pair, and 8 is the second.
3  8
4  11
5  14
6  17 and so forth
Question d.  If a number "n" is the first number, what is the second number?
I don't know how my son should answer this question. It sounds like it should be a formula but how does he get to it and how do I explain it to him.
Looking forward to your help.
Cheryl Answered by Janice Cotcher. 





A pattern 
20100901 

From Hien: How to find the pattern in this function?
x=1, y=o
x=2, y=1
x=3, y=1
x=4, y=2
x=5, y=2
x=6, y=3
x=7, y=3 and so on... Answered by Tyler Wood. 





A pattern in a puzzling sequence 
20100709 

From Martha: A1 2 3 B 5 6 7 C 9 10 11 D 13 14 15
USE THIS PATTERN SUGGESTED TO HELP YOU FIND
THE MISSING TERMS IN THE PROBLEM BELOW:
a) H _ _ _ b) R _ _ _
c) _ _ 50 _ d) _ _ _ 63
e) _ @#$ where @ + # + $ = 258 Answered by Tyler Wood. 





777777 times 111111 
20100707 

From Chew: What is 777777 times 111111 without using a calculator? Answered by Chris Fisher. 





A sequence 
20100127 

From Haku: if there are 8 dots in the first shape, 13 in the second, 19 in the third, and 26 in the fourth, then what is the formula? Answered by Penny Nom. 





Finding the Pattern in a Sequence 
20080916 

From sjp: please could you help me find the nth term for
8 4 0 4 8
and
4 1 4 11 20
Thank you Answered by Janice Cotcher. 





Mowing a Lawn in Concentric Bands 
20080905 

From Mari: two kids are mowing half of their backyard which is rectangular with
dimensions 75 ft by 90 ft. The first kid starts mowing at a corner
gradually working his way toward the middle by mowing concentric
bands around the outside edges.If the mower cuts 3ft wide path,
at what point should the first kid stop and the second kid start mowing?
THANKS! Answered by Janice Cotcher. 





Hidden Faces of a Row of Cubes 
20080825 

From Mhiko: how many hidden faces of a cubes are there in a 5 cubes in a row?
how many hidden faces of a cubes are there in a 10 cubes in a row?
how many hidden faces of a cubes are there in a 15 cubes in a row?
how many hidden faces of a cubes are there in a 20 cubes in a row?
please show me the solution or formula.... Answered by Janice Cotcher. 





Sum of Digits 
20080724 

From Warren: If 100^2525 is written in decimal notation, what is the sum of digits? Answered by Penny Nom. 





Powers of 2 
20071128 

From Kim: Complete the following:
2 to the power of 4=
2 to the power of 3=
2 to the power of 2=
2 to the power of 1=
If the pattern continues, 2 to the power of 0 = Answered by Penny Nom. 





Describe the pattern 
20070929 

From Baffled: Given a rule, extend a pattern and describe it in informal mathematical language:
a) 1, 6, 16, 36, _
b) 2, 6, 14, 30, _
c) 1, 8, 22, 50, _
d) 3, 9, 27, _
e) 2, 7, 17, 37, _ Answered by Stephen La Rocque and Penny Nom. 





Number pattern 8, 27, 64, ... 
20070912 

From Valerie: what is the number pattern 8,27,64, Answered by Stephen La Rocque. 





Pattern for a truncated cone 
20070511 

From Mike: I have been trying to get this cone flat so I can build this column. Can you please help me so I can figure this out? Thanks for your help. Answered by Stephen La Rocque. 





On day 1 on which day will 96 students donate food? 
20061119 

From Veydee: during a canned food drive the number of students who donate food doubles each day. If three students donate food on day 1 on which day will 96 students donate food? we have to find the term rule for this pattern Answered by Penny Nom. 





A number pattern 
20061002 

From Tim:
The patterns that went in 2s, 4s and 5s we got, but we are stuck on the pattern that doubles. We can't come up with the rule or equation that solves it.
With the first number being the term number and the second being the term, this is the pattern:
11
22
34
48
516
632
764
100128
What is the rule for this?
Answered by Stephen La Rocque and Penny Nom. 





Mathilda and Matthew 
20051218 

From A student:
Question: 1) The average of 12 is 5. The average of of 8 of these numbers ia 6. What is the average of the other four.
2)Mathilda is playing a mathematical game with Matthew. Each player starts from a point, then moves in a straight line to a second point,then to a third and so on. The moves are not made randomly, but are determined by a mathematical rule. The object of the game is to find the rule. It is Mathilda's turn to move on the grid . She starts at point M (3,9), moves to point N (2,4) and then to point O (0,0). Given Mathilda's rule, what could be the coordinates of the next point to which she might move?
Answered by Penny Nom. 





A pattern for a truncated cone 
20051204 

From Nick: I need to make a large cone segment. The large end has ID of 57 inches and the small end has ID of 23 inches. The cone is essentially a 45 degree cone (90 degrees at the tip). The sides of the segment are 2 feet long. How do I lay out a flat pattern that will fold into this segment? I need to know radius 1 and radius 2 and the angle the piece must be. Answered by Penny Nom. 





111111...111 divided by 3 
20051114 

From Jesus: If we divide the number 1111...........1( it has got 2004 digits) by 3. How many zeros will we get?. The answer that I have found in the book is 667 but I do not know how to reached it. Answered by Penny Nom. 





Frieze patterns 
20040519 

From Christina: How can I prove that there are only seven unique geometric frieze patterns? Answered by Penny Nom. 





A dressmaker's pattern 
20040227 

From A dressmaker: Does a dressmaker's pattern for a dress, such as a skirt made up of several pieces of isosceles trapezoid, qualify as a net? How about patterns for other types of clothing or accessories e.g. jackets, handbags?Ξ Answered by Diane Hanson. 





Two equations 
20030821 

From Jennifer:
The following problems have me stuck and any help would be greatly appreciated seeing my text book is doing me no favours:
3^{2a+1}  283^{a} + 9=0 and 5^{2m}  5^{m}=20 Answered by Penny Nom. 





x6square root of x +8=0 
20030510 

From Elizabeth: x6square root of x +8=0 Answered by Penny Nom. 





AABBBCCCCAABBBCCCC... 
20030209 

From Patty: The pattern AABBBCCCCAABBBCCCC continuously repeats. What is the 2003rd letter in the pattern? Please help, I am trying to figure out. Answered by Penny Nom. 





Transformations of pattern blocks 
20030206 

From Cheryl: I am trying to help my 8th grade son with Transformations  use of patttern blocks. He has to trace a figure and reflect it across the xaxis, which I can do, but then it indicates include ordered pairs  that confuses me. Answered by Penny Nom. 





A pattern in a table 
20021114 

From Thamar: how do you solve for pattern in a table like
the top row is  2  6  12  17  z  the bottom row is  9  13  19  24  blank  question ask in each blank space write a rule to find the next number in the table Answered by Penny Nom. 





A twelvevolume set of encyclopedias 
20021104 

From Ron: A novice librarian shelved a twelvevolume set of encyclopedias in the following order from left to right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and 2. Using her system, where will volume 13 go? Answered by Penny Nom. 





3, 6, 10, 15, 21 
20011129 

From Patrick: we are trying to find the expression to solve for the nth term in the pattern 3, 6, 10, 15, 21 Answered by Denis Hanson. 





Some algebra 
20011015 

From James: I cannot figure these out I was wondering if you could help me? I have no one to answer my questions.  (7x^{2} 3yz)^{2} (7x^{2} + 3yz)^{2}
 Use Pascals triangle to expand (2x y)^{4}
 8x^{3} y  x^{3} y^{4}
 (m + 3n)^{2} 144
 12x^{4} y 16x^{3} y^{2} 60x^{2} y^{3}
 p^{3} q^{2} 9p^{3} + 27q^{2} 243
Answered by Peny Nom. 





Find the pattern 
20010926 

From A parent: MY SON HAD ON A WORKSHEET WHAT I HAVE LISTED BELOW, BUT WE CAN'T SEEM TO FIND THE PATTERN. MOST THE TIME WE CAN, BUT THIS ONE IS DIFFERENT. 6,___, 9,____,____,_____,_____,_____ Answered by Caude Tardif. 





Taking matches 
20010505 

From Mark: Two piles of matches are on a table. A player can remove a match from either pile or a match from both piles. The player who takes the last match loses. If there are two players, how should you play? Answered by Claude Tardif. 





A sequence question 
20001023 

From Chell: I have the following sequence: 4 16 37 58 89 145 42 20 I have no clue how to arrive at an answer. I've checked to see if it can be defined as an arithmetic or geometric series, and it can't. I've looked for primes and noticed that 37 and 89 are the only primes ... but from there I've lost. Nothing I've tried seems to work, so please help! Thanks a million!!!! Answered by Chris Fisher. 





Tessellations 
20000917 

From Lindsay: What is the word that means a shape repeated over and over again to make something like a quilt pattern? Note: I'm pretty sure it is either a fractal or tesselation. Could it be that the pattern itself is a fractal but the entire quilt would be a tesselation? Answered by Chris Fisher. 





Factoring 
20000912 

From Melissa: I would like you to help me factor (x^{ 6}y^{ 6}) & (a+b)^{2}+3(a+b)4 Answered by Penny Nom. 





Three pattern questions 
20000822 

From Michael Rodriguez: I have 3 pattern questions that I need help answering, please.  6 and 7 = 42
2 and 5 = 10 4 and 8 = 8 5 and 9 = ?  7 and 5 = 1
9 and 12 = 3 10 and 15 = 5 12 and 16 = ?  1st = 1
3rd = DEF 10th = * 6th = ? Answered by Claude Tardif. 





Patterning and Sequencing 
20000705 

From Michael Jellis: What would be the next two terms? 1.0,0.5,0.6,0.75,0.8,___,____ please explain!!! I am completely baffled and need all the help I can get! Answered by Claude Tardif. 





The units digit of 3 to the 58th power 
20000510 

From Kylie Mcalpine: the questions we have been asked are what is the units digit of the following: a) 3^{58} b) 23^{58} c) 17^{31} and the harder question of: what is the units digit of the following sum: 13^{841} + 17^{508} + 24^{617} = ??????? Answered by Paul Betts and Penny Nom. 





Looking for a pattern 
20000508 

From Laura: Yesterday, me teacher stumped me with a question. He talked to us about square units. He told us an area of 1 square unit produces 1 shape, an area of 2 sq.units produces 1 shape, an area of 3 sq.units produces 2 different shapes, an area of four square units produces 5 different shapes, and an area od five sq.units produces 12 different shapes. He left us there. He said we had to find how many different shapes an area of 1 sq. unit produces through how many different shapes an area of 15 sq.units produces. He said we could complete this "chart" by finding an equation. But, I can't find the equation. I think it may be a quadratic of some sort. My teacher told us to use the area(in sq.units) as X and the # of different shapes produced as Y. Now, what really is stumping me is I would have to have an equation so when X is Y, Y is 1 and when X is 2, Y is 1. I have also tried to see if I can complete a patter or something. The pattern I saw was 1,1,2,5,12. I can't make much sense of that pattern. Answered by Penny Nom. 





Regular and irregular shapes 
19991003 

From Samuel Tighe: What is the difference between a regular shape and an irregular shape? Are a rectangle and a triangle regular or irregular shapes? Answered by Walter Whiteley. 





Inductive reasoning pattern 
19990913 

From Greg Walsh: What are the next 2 rows of the pattern? 3 13 1113 3113 2123 112213 312213 Answered by Walter Whileley. 





Patterns 
19990107 

From Melis Kalay: I'm confused about questions like these: 1. 2by2by2 cube: If this cube was painted blue on the outside,  how many cubes would have 3 blue faces
 2 blue faces
 1 blue face
 0 blue faces
Answered by Jack LeSage and Penny Nom. 





Geometry patterns lesson plans 
19981231 

From Vicki: hi,,, my name is Vicki and I am a new 5th grade teacher.... Anyway, I'm supposed to come up with a lesson plan to  Explore patterns that result from cominations of "reflections, rotations, and translations of geometric figures.
The plan is to include:  writing/metacognition, assessment strategies, interdisciplanary connections, supplemental materials, or textbook, and Bloom's taxonomy level.
Any help you could give would be greatly appreciated. Thanks Answered by Jack LeSage. 





Help the Helper 
19980920 

From John Derr: I am TRYING to help my niece with her Community College Teacher's math course! I have a BS and an Engineer yet stumble on what her book is asking:  Fill in the blanks to continue this sequence of equations:
1  =  0+1  1+3+1  =  1+4  1+3+5+3+1  =  4+9  _______________  =  ____  _______________  =  ____   What expression, suggested by part (1.), should be placed in the blank to complete this equation?
1 + 3 + 5.........+ (2n3) + (2n1)+ (2n3)+...+5 + 3+ 1  =  _________  Answered by Penny Nom. 





A Pattern 
19980914 

From Krystin: Question: 1=1x1 1+2+1=2x2 1+2+3+2+1=3x3 draw a series of diagrams to illustrate the above pattern Answered by Penny Nom. 





Frieze Patterns 
19980819 

From Brian Bairstow: I am doing a research project on frieze patterns (also called band patterns or border patterns). I know that there are exactly seven different types of frieze patterns, but I have been unable to find a proof for this. If you could tell me this proof, or tell me some internet sites on which I can find material on this, I would be very grateful. Answered by Chris Fisher. 

