Scrabble Grams

Hang 17 pictures

17*16*15*14*13*12*11*10*11*10*9*8*7*6*5*4*3*2*1=355,687,428

BassLady -
you are making up a problem .
OK, but in your diagram stem box
we would like to see a number for each of your 3 categories.

I have 10 - 3 peice outfits (10 skirts, 10 jackets and 10 blouses).  How many different ways can I wear them, assuming that each can be worn with the other.

So if I started with blue pants and changed the tops and bottoms - I have 100 choices for that color of pants.  10 * 9 + 10 = 100 per different color pants.

100 * 10 (colors) = 1000 different outfits that I can wear.

Soller - try again. List how many ways you can arrange 3 things on 3 shelves.
Is it 3*3=9? If not, your method does not work for larger numbers either.

21. how many ways can you arrange 21 pictures on 21 shelves?

21*21=441

Houdini - thanks for problem #26.
I did not know there were 26 briefcases on Deal or No Deal.

JooJoo - there are now 2652 blue tips on each circle.
That's 2652 too many!
Remember show each number in the stem box required in your calculation.
Is 2 in your calculation? Where? How did you get 2652?

Now there is 2652 points which would mean the songs to choose 2 songs from: (Sorry though there is so many that I don't think there is a way to count them

#26-How many different ways one person can choose to open the 26 briefcases on Deal or No Deal.

26x25x24x23x22x21x20x19x18x17x16x15x14x13x12x11x10x9x8x7x6x5x4x3x2=

403291461126605635584000000 different ways.

For the first briefcase opened there are 26 possible briefcases to choose, for the second there are 25, for the third there are 24...etc.

The last briefcase opened is only one choice, therefore it is not included and does not need to be.

Merry Christmas!!!

Melewen - that's a good problem for those of us with iPod shuffles.

Poovey - you are now saying there are only 2 ways to arrange the prisoners?
What sort of advice or formula would you give others who unhappily selected a trick question?

My head hurts with all this thinking.....

There would be two different rotations; clockwise, counter-clockwise

abc, bca, cba could just be starting positions to the rotations......

My question:

21. How many ways can you order 21 songs on a CD you're burning?

Answer: 21x20x19x18x17x16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1 = 5109094217e19

Aaand again, I'll do the doodle as soon as I can. The applet only really works on one computer I can use, so I have to wait to get there to be able to finish many of these problems. 

SkoolGirl - 1+11*10*9*8*7*6*5*4*3*2*1 = 39916801 on my calculator.
what were you doing? i still dont understand the 1+
is that for grandpa?
if grandpa eats dinner with only 2 relatives is the formula 1+2*1=3 ways?
list them and see.
then read Poovey's thinking on #3.

BassLady - make up a problem with the same idea as the others.

Fro - Zonino claimed #20 on the 15th
Hint: do your same problem with 21 computers.

Connect 20 computers on a network so that each computer is connected to exactly two other computers?

20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1=2,432,902,010,000,000,000 ways to connect those 20 computers.

Thanks Poovey.

Mr. Holt I fixed my radii, I think it's right now.  (In the same comment above)

Bubba- your (N-K+1) formula says the answer 17-17+1 = 1, not 355687428096000
How did you get 355687428096000?

Centerfield - copy the data for your flower as well, so we know how you drew it.

Poovey - What is the difference between bac and cba rotationally?

BassLady - Draco calimed it first. pick another.

JooJoo - you only drew 3 levels.
That's OK, but how many red tips do you have in your drawing?

Lexiowen - you showed your method. Now what is your answer?
copy the data for your flower as well, so we know how you drew it.

Zonino - i see you have done some thinking on #20:
Draw lines between 20 points so that each point is connected to exactly 2 other points?
Question: if you had only 4 points, would your answer be 2*1=2?
if not, then halving the number of points is not the way to go...
if it is, then you will be on your way to convincing me
with extra credit...

Trixie - nice doodling. looks like the backs of some playing cards i have seen.
however, note that you only drew 52*51*50
but that's OK as long as you tell us.

Melewen - now that you have seen the pattern of these problems,
make up your own problem and tell us which number it is...

Draw lines between 20 points so that each point is connected to exactly 2 other points?

In order to do this, I drew smaller diagrams to show the number of lines needed to connect n number of points so that each is connected to two other points.  I found that the # of lines that are needed is equal to the number of points.  So it would seem to me that since each point must connect by two lines, then there would only be half the number of possibilities..  thus:

10x9x8x7x6x5x4x3x2x1=3,628,800 ways.

8. Sing the first 8 notes of "Joy to the World".

Used 8*7*6*5*4*3*2*1

18. Deliver 18 pizzas to 18 homes starting from the Looloolo Pizza Hut?

You would use the 18x17x16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1

In this picture it looks like the LooLoolo pizza hut is in the middle and the houses are surrounding.

19.  Assign 19 different jobs to 19 workers?

Lets say there were 19 slots.  If one person held slot one - the other 18 could change jobs 18 different times.  Therefore there are 19 different jobs for each person.

19 x 19 = 361 different ways the jobs could be held - Assuming that all 19 jobs have to be held each time.  In other words different days there isn't just 2 jobs or 7 jobs.  Each day all 19 jobs are filled with 19 different people.

19. Assign 19 different jobs to 19 workers?

19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 = 1,21,645,100,400,000,000

Note: This picture only contains 19, 18, 17.

n! = (n * (n-1))*(n*(n-2))*(n*(n-3))....(n*(n-18))

n=19

Each time a job is given to one of the 19 people, that job is no longer available to be taken.

#16. Sequence 16 truth tables?

16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 =  2.092E13

hang 17 different pictures

(N-K+1) is the formula

N=17  K=17

ansower is 355687428096000

Mr.Holt,

I added a 1 at the end for the last person left to sit in the chair, if I multiply by 1 at the end the number would stay the same and not add that last person on.

#17 Hang 17 pictures

17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1= 355,687,428 ways

5. I am assuming that there is not a requirement to drive all of the roads.  If there is this is wrong.

The idea is that from the starting point (A) there are four options (B, C, D, or E). ie. 4.
From B, C, D, or E, there are three options (If you chose A then B your options are C, D, or E.)
Assuming you went to C after A and B you now have two options (D and E.)
If you took the easy route A then B then C then D, your only option is E.
And after that long trip you go back to A.

I think it works.

total you have 4x3x2x1 or 24 options.

ps I think I am having flower envy

There are 10 digits in a phone number if they can only be used 1 time each then the answer is 10*9*8*7*6*5*4*3*2*1=3,628,800

I took the chart at the top of the page and worked with that. After you stair at it for a while you figure out that all you do is multiply one number to the next. 1x1=1,2x1=2, 3x2=6, 4x6=24, etc.

1	1
2	2
3	6
4	24
5	120
6	720
7	5040
8	40320
9	362880
10	3628800

Thats how I did it. Maybe this will help some people.

Harkar - dont use ! in your explanation. some of us dont know what that is.
also in your drawing, you need as many radii and colors as you have stems
or your drawing will only draw the first 3 stems.
make sure to read each assignment.

Poovey - rotations makes sense. can you list all the rotations for us? thanks

Trixie - nice flower, however we are only seeing 3 colors and 3 radii,
so 52, 51, 50 is all that shows up in the stems.
The applet only draws as many stems as the box with least number.

Skoolgirl- why did you add a 1 at the ends of your equation?
1+11*10*9*8*7*6*5*4*3*2+1 =39,916,802
Say only 3 people show up for dinner.
Would your equation be 1+2*1+1=4 ways to seat everyone.
Read Poovey's problem.
Also - your flower reminds me of some thanksgiving puddings i have known.

12. Seat 12 players at a round Thanksgiving table relative to each other?
     Grandpa always sits in chair A.

seats: A   B   C  D E  F  G  H  I  J  K  L 

         1+11*10*9*8*7*6*5*4*3*2+1 =39,916,802

Since Grandpa always sits in chair A, chair B has 11 people who can sit in it, once chair B has someone in it it only leaves 10 people to sit in chair C and so on.

 #2 Shuffle a 52 card deck?

Since there are 52 cards in a deck, the cards can be in 52 different positions.

52*51*50*49*48*47*46*45*44*43*42*41*40*39*38*37*36*35*34*33*32*31

*30*29*28*27*26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*

9*8*7*6*5*4*3*2*1= 8.0658175170943878571660636856404e+67

#6. How many ways can you arrange the letters of the alphabet?

26!=26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1=
4.032914611266057e+26

The number of ways of arranging n unlike objects in a line is n!.
n! = n × (n – 1) × (n – 2) ×…× 3 × 2 × 1

This is because there are twenty-six spaces to be filled. The first space can be filled by any one of the 26 letters. The second space can be filled by any of the remaining 25 letters. The third space can be filled by any of the 24 remaining letters,etc.

Maybe I should have all of you name the species of flower that you creating?

Pac - nice blue gysumism.

Sunshine - dont know what to call yours.

Melewen - Sunshine beat you to it. Pick another.

14. Shelve 14 books?

14x13x12x11x10x9x8x7x6x5x4x3x2x1= 87178291200

again, i'll do the picture once i find an able computer 

Shelve 14 books?

n=14 x n-1 x n-2 x n-3............

This = 87178291200

I represented my flower with 4 variables due the complexity.

May I recommend not trying to make a flower with 15,14,13,12,11,10,9,8,7,6,5,4,3,2,1.  My computer is pretty powerful and I had to restart it after it froze 45 minutes into drawing it.  :-)

Never fear, I've followed 7Iron's lead and used five numbers (15,14,13,12,11), which only took a second to draw.

#15 was 15 people in 15 places, which is 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 = 1,307,674,368,000.

The updated flower is:

Poovey - it is not a matter of correctness,
but of seeing there is a difference sometimes
and no difference in others.
If yo were the warden,
and drew the order the prisoners were in,
would ABC or CAB be different orders?
So under this new consideration,
how many orders are there?

Tiger - some of those digits cannot be used in some postitions.

7Iron - nice flower!

13. Stack 13 boxes

13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 6, 227, 020, 800

If you have 13 boxes and they are on one stack, you can arrange them by doing

 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 which gives you 6, 227, 020, 800

The formula for this would be n=13      n(n-1)(n-2)(n-3).......(n-12)=

I only used 4 numbers to show the example

#7  There are 10 digits in my phone number including area code.

So there are 10 possible numbers in each place.

10*10*10*10*10*10*10*10*10*10=10000000000

Well I guess looking at it that way, it could mean that the three prisoners, no matter what position since it is a triangle, would be the same just shifting in a circular direction.

Is that correct?

SuperDuke -
I would accept your illustration if it showed at least 3 numbers starting with 50.
Experiment with various radii , like 1, .75, .01
Thanks.

Harkar - i dont see the number 26. Where is 10 in your solution?

#6. How many ways can you arrange the letters of the alphabet?

26!=26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1=
4.032914611266057e+26

The number of ways of arranging n unlike objects in a line is n!.
n! = n × (n – 1) × (n – 2) ×…× 3 × 2 × 1

This is because there are twenty-six spaces to be filled. The first space can be filled by any one of the 26 letters. The second space can be filled by any of the remaining 25 letters. The third space can be filled by any of the 24 remaining letters,etc.

Note on flower applet: To make it easier to see I only used 10 letters.

#1 How many ways can you visit the capitals of each of the fifty states?

I am going to visit the first three states only in order to be able to render this.

If we begin in the center we have 50 lines (possible states) to choose from. upon moving to one of those states we would then have 49 possible states to choose from ( the blue lines), uon reaching this destination, we would have 48 states left to choose from ( the red dots are actual 48 lines each). this would continue on down as you choose each new state( although graphically we can't render it in a way you can see).

The actual problem is with 50 states. It would look like this only it would be 50*49*48*47*46*45*44*43*42*41*40*39*38*37*36*35*34*33*32*31*30*29*28*27*26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1=             3.0414093201713378043612608166065e+64 (by the way this is a big number!)

We don't want to even talk about the flower, I'm not fryin my AMD for it. ;-)

UPDATED 11/11/06

Poovey - there is no difference between arrangements
123
231
312
why?

DirtyBird -
Show us your thinking.
Others may benefit.

Kathi -
I see the numbers 4 3 and 2 on your flower
but if you do not tell it another radii and color
we will never see the 1 on your flower
However, you are not required to do anymore on this.

1. #4. Seat 4 ladies in 4 chairs?

24 different ways

In Eng. you can take the number of ladies n and multiply it by the number of ladies minus K.

n(n-1)(n-2)(n-3) 

4(4-1)(4-2)(4-3) 

4 * 3 * 2 * 1 = 24

Pac - if there are 1,307,674,368,000 ways,
then why are there only 15x15 tips on your flower?
Did you represent the solution adequately?

DirtyBird - tell us how you got that.
Also review why this is a trick problem.
Look at #3.
Remember: grandpa always sits in seat A.
And what does 10x12 have to do with your solution.
Does your flower reflect your procedure?
Look at some other flowers and think about it.

15. Queue 15 people in a ticket line?

This is just the number of ways that these 15 people can be arranged in a line.  So there are 15 people and 15 different places that each person could be.

15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 = 1,307,674,368,000

So, there are over a trillion ways to organize these people in a line?  That sounds really high in my opinion, but that's what the math websites say too.

11. Place 11 football players in 11 positions?

 11*10*9*8*7*6*5*4*3*2*1= 39916800

 When you have 11 players, you can pick one player out of 11 to place in the first position. And you can pick one out of 10 players to place in the second position since one player is already in the first position. And you can pick one out of 9 to place in the third position since you already place two players in the first and second postions. So you have one less players to pick as you place them to each position. And you do that until you have one player left to place in the last position.

n * n-1* n-2 *...*n-(n-1)

Slick - tell us how you did  yours without using any symbols except + - * /.
NPR is National Public Radio.

Kathi - thanks for the further explanation.
How would you draw a flower
so that all those numbers you multiplied by would get into the picture?

Boki - thanks for simplifying it for us.
Delete your previous comment.

I'm not real sure on how to make it into a formula but here is the way I got the answer:

The way I have it figured is as follows:

1 lady, 1 chair: 1 outcome

2 ladies multiplied by the 1 outcome above = 2 outcomes

3 ladies multiplied by the 2 outcomes above = 6 outcomes

4 ladies multiplied by the 6 outcomes above = 24 outcomes

5 ladies multiplied by the 24 outcomes above = 120 outcomes

 9) Place 9 baseball players in 9 positions?

   Answer: 362880

Permutation problem: nPr

Kathi - if you had 5 ladies to arrange in 5 chairs,
how would you extend your method without a table?

Poovey - can you list all 9 positions to convince us of your method?
Also tell us about your method? How did you get 9?

#3   Place three prisoners in a triangle in three different positions; makes 9 different combinations

Without the 3 ladies problem I would have still constructed a truth table in order to find all possiblities, for me this is the easiest way to find the answer.

I use 1 as the test subject and only rotate the others in order to find the different combinations 1 object can have. 

Each of the 4 objects has 6 possible combinations of order if you leave one in the same place. Because of this you take the total number of objects (4) multipy times the number of combinations (6) and end with a total outcome of 24 possible combinations for all 4. 

1. #4. Seat 4 ladies in 4 chairs?

24 different ways

6 combinations for each individual lady = 24 out comes.

In Eng. you can take the number of ladies n and multiply it by the number of combinations to equal the number of outcomes. If lady A can sit with 3 other ladies 6 different ways then 4 ladies * 6 ways = 24 

Let n = # of ladies

Let w = # of combinations

n*w = total outcome