SUPER BOWL XXXII, January 19-23, 1998

On Sunday January 25, 1998 Super Bowl XXXII will be played in San Diego, California. The Super Bowl committee has decided to create a plaque to hang in the NFL Hall of Fame.

The plaque will have each Super Bowl title spelled out in gold letters like this:

SUPER BOWL I

SUPER BOWL II

SUPER BOWL III

. . . and so on . . .

SUPER BOWL XXXII

The winning team will have their name placed on the plaque in black letters. Some of the committee members are worried about the cost of the gold letters.

Your job is to determine how many of each letter or symbol must be made in gold. Do not count spaces or any of the black letters.

Be sure to explain how you found your answer.

As a Philadelphia Eagles fan I am having a little trouble trying to decide which team to back on Sunday. Can you give me any advice?

 

Comments from Mrs. B.:

Thanks for all the great advice on how to pick my team.

Reading this problem carefully you will see that you were being asked to find the number of each letter or symbol used. Many students submitted solutions which only told me that there were 390 total letters.

The correct answer needed to state that each letter S, U, P, E, R, B, O, W, L is used 32 times and the Roman Numeral I appears 45 times, V appears 15 times, and X appears 42 times.

Make a chart for the numbers 1 to 32 written as Roman Numerals and list the number of I's, V's and X.s and see what patterns you can discover.

Here is the start of the chart.

Number	Roman Numeral	I's	V's	X's
1	I	1	0	0
2	II	2	0	0
3	III	3	0	0
4	IV	1	1	0
5	V	0	1	0
6	VI	1	1	0

Keep Problem Solving

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A list of everyone who sent in a correct answer follows the highlighted solutions below, and more of the solutions are also available.

 

Highlighted Solutions

From:   Danny Koblenzda
Email   
Grade:  4
School: Charles E. Smith Jewish Day School, Rockville, Maryland

These are the numbers of letters needed.

S  32
U  32
P  32
E  32
R  32
B  32
O  32
W  32
L  32

I  45  (14 in each group of ten times 3 groups of ten plus 3 from 
        the thirties)
V  15  (5 in each group of ten times 3 groups of ten plus 0 from 
        the thirties)
X  42  (I just counted)

Total letters:  390

Go Redskins!

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From:   Annie Roth 
Email   
Grade:  8
School: Frenchtown Junior High: Frenchtown, Montana

Hello! :o)

Super Bowl is spelled with 9 different letters. There aren't two of any 
letter so if Super Bowl is spelled out 32 times then there will be 32 
of each letter.  

To get the number of letters for the number symbols (Xs, Vs, and Is) 
I wrote out a list. The list starts at the first Super Bowl, or I.  
The numbers are written out in Roman Numerals:

     I       XII     XXIII
    II      XIII      XXIV
   III       XIV       XXV
    IV        XV      XXVI
     V       XVI     XXVII
    VI      XVII    XXVIII
   VII     XVIII      XXIX
  VIII       XIX       XXX
    IX        XX      XXXI
     X       XXI     XXXII
    XI      XXII
	
If you count how many Is and Vs and Xs you will get the following 
numbers for each:
	
    X: 42 of this symbol
    V: 15 of this symbol
    I: 45 of this symbol

Here is a complete list of  all the letters and symbols and how many 
of each there are. (If you add them all up, you will see the total 
gold letters and symbols that will need to be made.)

    S: 32
    U: 32
    P: 32
    E: 32
    R: 32
    B: 32
    O: 32
    W: 32
    L: 32
    X: 42
    I: 45
    V: 15
   +______
      390

As for which team to cheer for, I'm for the Green Bay Packers myself.  
Hey, Wisconsin's closer...why not!?! :o)  =+>

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From:   Mrs. Russell's Geometry class
Email   
Grade:  8
School: Murray Hill Middle School

The way that we solved this problem was by writing it out.

When we wrote it out we found out that there were 32 s's, 32 u's,
32 p's, 32 e's, 32 r's, 32 b's, 32 o's, 32 w's and 32 l's.
When we counted the Roman numerals we found out that there were 
45 I's, 42 X's, and 15 V's.
The number of gold letters that we counted after we had added the 
total number of letters and Roman numerals was 390.

After the class read that you were having a difficult problem 
finding out who to root for we decided that you should root for 
the Denver Broncos. You should root for them because John Elway
has been to the Super Bowl 4 times before and hasn't won one yet.
It would be a nice ending touch to his Hall of Fame career. 

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From:   Brian Hunter
Email   
Grade:  6 (Mrs. Buchholz Class)
School: Paul Laurence Dunbar Middle, Ft. Myers, FL

There are Thirty-Two Super Bowls. The word "Super Bowl" has no letters 
that are the same. If each letter in Super Bowl is equal to one, then 
there would be 32 of each letter.

    S=1, u=1, p=1, e=1, r=1, B=1, o=1, w=1, l=1.
    x32  x32  x32  x32  x32  x32  x32  x32  x32
---------------------------------------------
32S's, 32u's, 32p's 32e's 32r's 32B's 32o's 32w's 32 l's.

The numbers in the Super Bowl Names are in Roman Numerals.  
Here are the figures:

I: 1-9 there are 14 ones. 11-19 there are 14. 20-29 there are 14.  
30-32 there are 3. There are 45 I's needed.

V: 1-9 there are 5. This is the same with 11-19 and 20-29. There
are no V's in 30-32. There are 15 V's needed.  

X: In 1-9 there is 1 X. In 10-19 there are 11. In 20-32 there are 30.  
There are 42 X's needed.

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From:   Marcus VanGrinsven and Isaac Hendrickson
Email   
Grade:  8
School: Nedrose School, Minot, ND

The total of gold letters and/or symbols will be 390.
The breakdown for each is as follows:

32 of each letter in the words "Super Bowl" = 288

The symbol V = 15
The symbol X = 42
The symbol I = 45

First we multiplied 32 x 9 (number of letters in Super Bowl)

Then we listed each Super Bowl year out in Roman numerals.
Then we counted each X, V, and I.

Then we totaled for the grand total of 390.

Comment:  Sounds pretty expensive!

Grade 8 Math Whizzes - Nedrose School

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From:   Mrs. Kortan's Algebra Class
Email   
Grade:  8th Grade
School: Edison Middle School, Sioux Falls, SD

This was a good one because it deals with football.  

The way we got this is that we took all of the letters in Super 
Bowl and you would need 32 of each. All put together you would 
need 288.

The following is a chart showing the Roman numerals for the
numbers 1 to 32:

1=I 2=II 3=III 4=IV 5=V 6=VI 7=VII 8=VIII 9=IX 10=X 11=XI 12=XII
13=XIII 14=XIV 15=XV 16=XVI 17=XVII 18=XVIII 19=XIX 20=XX 21=XXI
22=XXII 23=XXIII 24=XXIV 25=XXV 26=XXVI 27=XXVII 28=XXVIII 29=XXIX
30=XXX 31=XXXI 32=XXXII

There are 45 I's  15 V's and 42 X's.  There are 32 each of the 
letters in SUPERBOWL that will have to be gold.

I would go for Green Bay* because your team has the same colors.
You could wear one of your Eagles shirts turned inside out while
you are rooting for the Packers! By the way, the Super Bowl is on 
the 25th, not the 26th!

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From:   Heather Roka
Email   
Grade:  6
School: Paul Laurence Dunbar Middle, Ft. Myers, FL

S-32 U-32 P-32 E-32 R-32 B-32 O-32 W-32 L-32 I-45 V-15 X-42
 
I figured this out by adding 32 SUPERBOWL games, and none of them 
repeated. Then I wrote out all the Roman numerals up to 32 and 
counted them, except for V because I knew there were 5V's for every 
set of ten.

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From:   Mrs. Kortan's Pre-Algebra Class
Email   
Grade:  7th Grade
School: Edison Middle School, Sioux Falls, SD

I'm not sure how much each letter or symbol will cost, but I  don't 
think they're going to have any trouble paying for it. I think that 
the answer could be better explained in a graph so...

S = 32
U = 32
P = 32
E = 32
R = 32

B = 32
O = 32
W = 32
L = 32

We found this because there are going to be 32 Super Bowls counting 
this year and there is one of each letter per Super Bowl.

As for the symbols, we decided to tally for lack of a better method.  
We found that there would be forty-five I's, fifteen V's, and forty-two 
X's. In all, there would be three hundred ninety letters or symbols.  

As far as who you should go for, I would have to say the Denver Broncos.  
I say this because I'm lactose intolerant, and with Green Bay being the 
cheese-capital of the world and all...

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From:   Mike Bockus
Email   
Grade:  9th
School: John Shero Jr. High

The words SUPER BOWL will be printed 32 times and there are 
9 letters in those words, making a total of 288 gold letters.

I wrote down the Roman numerals from 1 to 16 when I noticed a pattern.
For the numbers 1 to 9 you will need 14 Is, 5 Vs, and 1 X for a total 
of 20 gold letters.

For the numbers 10 to 19 you will need the same as 1 to 9 with an 
extra 10 Xs for a total of 30 gold letters.

For the numbers 20 to 29 you will need the same as 1 to 9 with an 
extra 20 Xs for a total of 40 gold letters.

For 30 to 32 you will need 9 Xs and 3 Is for a total of 12 gold 
letters.

So overall you will need 288+20+30+40+12 = 390 Gold Letters.

So you will need 32 of each letter SUPER BOWL.
You will need 42 Xs.
You will need 15 Vs.
You will need 45 Is.

Go Bronchos, I hope we finally win one! - Mike

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From:   Neil Bress
Email   nbress @ aol.com
Grade:  6 to 8
School: Morgan Village Middle School, Camden, NJ

A perfect problem for my sixth graders. We looked at Roman Numerals as 
a counting system, and looked to identify patterns.

The students agreed that since each letter in the words SUPER BOWL are 
different, there would be 32 of each.

The Roman numerals were more challenging. We split up into 3 groups; 
Group 1 was responsible for 1-10, Group 2 from 11-20 and Group 3 from 
21-30. As a class, we added 31 and 32 to our totals. Here's what 
Section 6101 came up with:

Group 1 - 14 I's, 5 V's and 2 X's
Group 2 - 14 I's, 5 V's and 12 X's
Group 3 - 14 I's, 5 V's and 22 X's
Combined Class - 3 I's and 6 X's.

Our totals:

32 each of S - U - P - E - R - B - O - W - L   (288)
45 of I  (45)
15 of V  (15)
42 of X  (42)

Total letters to be ordered:  390

Section 6101 at Morgan Village Middle School in Camden, NJ suggests you 
root for Green Bay, because "Da Packers are Da Bomb!"

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From:   Jay Gill
Email   
Grade:  8
School: Nichols Middle School, Buffalo, NY

There are nine letters in "Super Bowl".  None of them are Roman 
numerals: X, V, or I. Each of them must be made 32 times.

   Roman Numerals
(Assuming 4 is IV(not IIII) and 9 is IX(VIIII)).
#     I    V    X       
1     1    0    0
2     2    0    0
3     3    0    0
4     1    1    0
5     0    1    0
6     1    1    0
7     2    1    0
8     3    1    0
9     1    0    1
10    0    0    1
11    1    0    1
12    2    0    1
13    3    0    1
14    1    1    1
15    0    1    1
16    1    1    1
17    2    1    1
18    3    1    1
19    1    0    2
20    0    0    2
21    1    0    2
22    2    0    2
23    3    0    2
24    1    1    2
25    0    1    2
26    1    1    2
27    2    1    2
28    3    1    2
29    1    0    3
30    0    0    3
31    1    0    3
32    2    0    3
Tot. 45   15   42
Answer:
Letter   # Required
B         32
E         32
I         45
L         32
O         32
P         32
R         32
S         32
U         32
V         15
W         32
X         42

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The following students submitted correct solutions this week:

June Lin, Grade 5th Grade, Sahuaro Elementary School/Phoenix/Arizona
Danny Koblenzda, Grade 4, Charles E. Smith Jewish Day School, Rockville, Maryland
Annie Roth , Grade 8, Frenchtown Junior High: Frenchtown, Montana
fish, Grade 5-8, hc crittenden middle school/Armonk/NY
Matthew Rogan and Jacob Raim and Harrison Miller, Grade 6, Georgetown day school, Washington DC.
Danielle Larsen, Grade 8th, O'Donnell Middle School/Stoughton/Mass.
Kym A. Apicelli, Grade 6th, Clark Lane Middle,Waterford, CT
Just Plain Stupid, Grade 5-AG, Clemmons El. Clemmons, NC
Bryce Laubenstein, Grade 6, Nitschmann Middle School Bethlehem PA
Torrance Flynn, Grade 6, Highlands Elementary, Saugus, CA
PAT DONALDSON, Grade 6, PAUL LAURENCE DUNBAR MIDDLE SCHOOL/FORT MYERS/ FL
Shane Mace , Grade 6, PLDMS/FT.MYERS/FL.
Mrs. Galler's class 6-6, Grade 6, Hobby Middle School San Antonio, Texas
Junichiro's Gang, Grade 8th Grade, American school of Paris
Mrs. Russell's Geometry class, Grade 8, Murray Hill Middle School
ANONYMOUS, Grade 5-AG, CLEMMONS EL., CLEMMONS, NC
Brett Wortzman, Grade 8, O'Donnell Middle/Stoughton/MA
Brian Hunter, Grade 6 (Mrs. Buchholz Class), Paul Laurence Dunbar Middle, Ft. Myers, FL
Joshua Wood, Grade 6- Mrs. Buchholz class, Paul Laurence Dunbar Middle School/Ft. Myers/FL
Christline Remy, Grade 6 Mrs. Buchholz Class, Paul Laurence Dunbar Middle School/Ft. Myers/ Fl
RobRoy MacInnes, Grade 6- Mrs. Buchholz class, Paul Laurence Dunbar Middle School/Ft. Myers/Fl
Cecilia Ekperi, Grade Grade 5, Georgetown Day School/Wash.DC/DC
Sarah Howard, Grade 8, FrenctownJr. High, Frenctown MT
Keith Ginoff, Grade 7, Frenchtown Middle School MT
JAKE ZEIMET, Grade 7, Frenchtown JH Frenchtown,MT
Zak Pulliam, Grade 8, Frenchtown J.H. Frenchtown, MT
Sarah Long, Grade 7th, Frenchtown Middle School, Frenchtown, MT
Elizabeth, Grade 5, Academy Hill School,Wilton,ME
Joanne Kelly, Grade 6th grade Mom!, Fitch Middle School, Groton, CT
Erin M. Ross, Grade 7th grade, E.V. Cain/Auburn/California
Travis Skeel, Grade 7 - Mr. Ross, Rocky Run Middle School Fairfax, Va.
Smart Owls, Grade 5, Agnes Irwin School/Rosemont/PA
Nicole.T, Grade 7, OZAUKEE
Renee Cutaia, Grade 6 {Mrs. Buchholz Class}, Paul Laurence Dunbar Middle School/Ft.Myers/FL
Marcus VanGrinsven and Isaac Hendrickson, Grade 8, Nedrose School, Minot, ND
Aneil Baron , Grade 5th grade, Georgetown Day School
Rimal Kacem, Grade 5th grade, Georgetown Day School Washington D.C.
Shawna Nelson and Justine Trueblood, Grade 5, Webster City Middle School Webster City, IA
Caleb Lande and Josh Johnson, Grade 8, Frenchtown Junior High\Frenchtown Montana
Nathan Strauss and Brian Powers and Ariel Franks and Nate Litz, Grade 4, Forsyth/St. Louis/MO
Brian Matthews and Min Wang and Jen Keiser and Casey Jenkins, Grade 8, Dodd/Cheshire/CT
Mrs. Kortan's Algebra Class, Grade 8th Grade, Edison Middle School, Sioux Falls, SD
Heather Roka, Grade 6, Paul Laurence Dunbar Middle, Ft. Myers, FL
Huma Awan, Grade 6, Paul Laurence Dunbar Middle/Ft. Myers/FL
Sarah Mcander, Grade 6-Mrs.Buchholz Class, Paul Laurence Dunbar Middle School/Ft.Myers/Fl
Mrs. Kortan's Pre-Algebra Class, Grade 7th Grade, Edison Middle School, Sioux Falls, SD
Michael Jordan, Grade 6 Mrs. Buchholz class, Paul Laurence Dunbar Middle School/Ft,Myers/FL
Joel Abbott, Grade 5, Webster City Middle School Webster City, IA
Juliann DiBenedetto, Grade 6, Paul Dunbar Middle School/ Ft. Myers/Fl
Brandon Ford, Grade 6, Paul Laurence Dunbar Middle School/ Ft. Myers/ Fl
Mike Bockus, Grade 9th, John Shero Jr. High
Molly, Grade 7, Our Lady of Lourdes/Slidell/LA.
christopher mayle, Grade 6th, Pl dunbar
Lesley Burkert, Grade 6th, P.L.D.M.S. / Ft. Myers, FL
Neil Bress, Grade 6 to 8, Morgan Village Middle School, Camden, NJ
Daniel Pfau, Grade 8, RFMS_Flemington_NJ
Kenny Siggs, Grade 6, PLDMS/Fort Myers/Fl
Natko Bajic, Grade 7, Pojisan Primary School, Split, Croatia
Anjali Sareen, Grade 6, P.L. D. M. S. , Ft. Myers,FL
Alexandra Morosan, Grade 6, Bayview Middle School, ON, Canada
Mrs. Galler's class 7-7, Grade 6, Hobby Middle School San Antonio, Texas
Mrs. Galler's class 7-9, Grade 6, Hobby Middle School San Antonio, Texas
Mrs. Galler's class 2-2, Grade 6, Hobby Middle School San Antonio, Texas
Mrs. Galler's class 1-6, Grade 6, Hobby Middle School San Antonio, Texas
Mrs. Galler's class 1-8, Grade 6, Hobby Middle School San Antonio, Texas
Mrs. Galler's class 1-7, Grade 6, Hobby Middle School San Antonio, Texas
Mrs. Galler's class 1-4, Grade 6, Hobby Middle School San Antonio, Texas
Chelsea Lofts, Grade 8, Frenchtown Jr. High, Frenchtown, MT
Jay Gill, Grade 8, Nichols Middle School, Buffalo, NY
Aaron Tjoa, Grade 8, Nichols Middle School/Buffalo/NY
David D, Grade 4, Ces/JDs/Rockville/MD
Traci Gibbs, Grade 7th, Frenchtown Junior High

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