Recreational Math

YummyCookies

sorry for repeating the answer!

Posted 142 day ago

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YummyCookies

just wanted to know......................if matherapist's answer chosen as the best answer, then that should mean that he or she should have received the $20.00! But matherapist wanted to donate that money to animal shelter...............................so did u donate that money to the animal shelter? i dont want any attitude to the answer, but just say yes or no! Thats all i am asking of u!
Thank You!

Posted 142 day ago

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YummyCookies

just wanted to know......................if matherapist's answer chosen as the best answer, then that should mean that he or she should have received the $20.00! But matherapist wanted to donate that money to animal shelter...............................so did u donate that money to the animal shelter? i dont want any attitude to the answer, but just say yes or no! Thats all i am asking of u!
Thank You!

Posted 142 day ago

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YummyCookies

just wanted to know......................if matherapist's answer chosen as the best answer, then that should mean that he or she should have received the $20.00! But matherapist wanted to donate that money to animal shelter...............................so did u donate that money to the animal shelter? i dont want any attitude to the answer, but just say yes or no! Thats all i am asking of u!
Thank You!

Posted 142 day ago

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YummyCookies

just wanted to know......................if matherapist's answer chosen as the best answer, then that should mean that he or she should have received the $20.00! But matherapist wanted to donate that money to animal shelter...............................so did u donate that money to the animal shelter? i dont want any attitude to the answer, but just say yes or no! Thats all i am asking of u!
Thank You!

Posted 142 day ago

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YummyCookies

just wanted to know......................if matherapist's answer chosen as the best answer, then that should mean that he or she should have received the $20.00! But matherapist wanted to donate that money to animal shelter...............................so did u donate that money to the animal shelter? i dont want any attitude to the answer, but just say yes or no! Thats all i am asking of u!
Thank You!

Posted 142 day ago

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YummyCookies

just wanted to know......................if matherapist's answer chosen as the best answer, then that should mean that he or she should have received the $20.00! But matherapist wanted to donate that money to animal shelter...............................so did u donate that money to the animal shelter? i dont want any attitude to the answer, but just say yes or no! Thats all i am asking of u!
Thank You!

Posted 142 day ago

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YummyCookies

just wanted to know......................if matherapist's answer chosen as the best answer, then that should mean that he or she should have received the $20.00! But matherapist wanted to donate that money to animal shelter...............................so did u donate that money to the animal shelter? i dont want any attitude to the answer, but just say yes or no! Thats all i am asking of u!
Thank You!

Posted 142 day ago

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YummyCookies

just wanted to know......................if matherapist's answer chosen as the best answer, then that should mean that he or she should have received the $20.00! But matherapist wanted to donate that money to animal shelter...............................so did u donate that money to the animal shelter? i dont want any attitude to the answer, but just say yes or no! Thats all i am asking of u!
Thank You!

Posted 142 day ago

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YummyCookies

just wanted to know......................if matherapist's answer chosen as the best answer, then that should mean that he or she should have received the $20.00! But matherapist wanted to donate that money to animal shelter...............................so did u donate that money to the animal shelter? i dont want any attitude to the answer, but just say yes or no! Thats all i am asking of u!
Thank You!

Posted 142 day ago

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YummyCookies

didnt have to show tht attitude, u know!

Posted 149 day ago

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matherapist

comment on samzappolas solution

You have demonstrated the solution for a non replacement version of the propblem.

The better analysis is to recognize that the 120 possible outcomes all have odd digits 1,3,5,7,9 in each column and that there are 24 repititions. You can then see that each column sums to 600 and add the appropriate zeroes for the 10's, 100;s and 1000'3 and get 666600 as an answer. Also you can use the analysis of math fanatics BF and use 5555 x 120 = 666600. Both of these involve a lot less effort.

M

Posted 150 day ago

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YummyCookies wants to know if $20.00 is real money?
Yes it is !!!! rajbaba78

Posted 150 day ago

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YummyCookies

is this $20 for real?

Posted 150 day ago

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math_fanatic

Comment on Amar Soni's use of mathematical progression:

For every group of 5 numbers you will have a common difference of 2 but then you will jump 12 to get to the next group of 5. Then after every 5 groups you will jump 112 to get to the next number. After every 25 groups of 5, you will jump 1,112 to get to the next number in the series.

Let's look at a few examples:

1111
1113
1115
1117
1119

+12

1131
1133
1135
1137
1139

+12

1151
1153
1155
1157
1159

+12

1171
1173
1175
1177
1179

+12

1191
1193
1195
1197
1199

+112

1311
1313
1315
1317
1319...

If we look at the last term that begins with a 1 and the first term that begins with a 3 you will see that
there is a difference of 1112: last term begins with 1 = 1999, first term begins with 3 = 3111

3111-1999 = 1112

This pattern repeats throughout the series. The formula you used was for a mathematical progression with a COMMON difference. But there is no common difference in this series. We aren't adding up all the odd numbers between 1111 and 9999. If we were, your answer would be correct.

Posted 152 day ago

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math_fanatic

I apologize for getting matherapist's background wrong. I thought he said in a previous post that he taught math for many years.

I do think his answer was a more efficient way of getting to the answer than mine was, however, I also think my boyfriend's answer was incredibly creative.

I think it's silly to do this for money though. I want to learn how to solve problems cleverly. That's more of a reward than money.

I've been having fun just figuring out the problems raj and matherapist have posted without the enticement of monetary compensation.

Also, none of us know the educational background of anyone else on the site. Some people may be at a much greater advantage than others. It's pretty obvious from the answers given that the ones given by the tutors (and my bf who's a lawyer and a science/math genius) are the ones that are correct. We clearly have the upper hand, though I think Raj and Matherapist have a little more experience than I do.

My point is that someone with a Ph.D. could come along and answer all the $20 questions. How fair would that be? I think Raj should consider just choosing the best answer by selecting it so it shows up at the top the way he did with mine in the even-numbered address problem. Some students may not be willing to compete for just a "gold star" but I don't like the mercenary aspect of these problems.

My background, for the record, is that I have an A.A. degree in general science. I took the full course of calculus, intro to linear algebra, and elementary diff. equations. This puts me at the level of being a junior in a math major at a 4-year college. I had to drop out 9 years ago due to a chronic illness but I still love math and I have been tutoring off and on for 3 years. I tutor algebra mostly because that's what kids seem to have the most trouble with. Because of that, my higher math skills have diminished with time, but I can factor polynomials like nobody's business.

Posted 152 day ago

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Amar Soni

The first number will be=1111 and the last number will be 9999 and the common difference is 2 using A.P. formula
last term= first term+(n-1) common difference
9999=1111+(n-1).2
n=4445
Therefore number of terms=4445
To find sum
Sum = n/2{2a+(n-1)d}
=4445{2*1111+(4445-1)82}=26,691,975

Posted 153 day ago

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matherapist

Raj & Math fanatic

Disqualify me as I do not accept $$ for this sort of thing. I think math fanatics BF's answer is very clever and they should get the prize.

One correction to math-fanatics assumtion about me- I have never taught in a classroom except for a physics Lab at a tech college last year. I have tutored math for the past 4-5 years. My ed is in Physics which is mainly applied mathematics or perhaps physics is the driver for mathematical development.

M

Posted 153 day ago

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math_fanatic

I have another answer that was given to me by my boyfriend (whose IQ is not measurable) who was able to do this problem and the calculation in his head in less than 3 minutes.

a) The easy part. The number of 4 digit numbers is 5^4 = 625

b) Here's where he's scary smart. The average of 1,3,5,7,9 is 5. Since there's the same number of each digit in each column, the average value of each digit is 5 so you can assign each digit a value of 5.

For each of the four columns the following will be true:

There are an equal number of 1's, 3's, 5's, 7's, and 9's so the average digit has a value of 5.
So for purposes of addition we can assign every digit in the 625 numbers a value of 5.
Now instead of adding 625 different numbers, we can simply multiply 625 by 5,555.

625*5,555 = 3,471,875

This is the same number Matherapist and I got for the sum of all the numbers.

Posted 153 day ago

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samzappala

There are 120, 4 digit numbers from the given digits.

The sum is 666,600.

1357 1735 3157 3715 5137 5713 7135 7513 9135 9513
1359 1739 3159 3719 5139 5719 7139 7519 9137 9517
1375 1753 3175 3751 5173 5731 7153 7531 9153 9531
1379 1759 3179 3759 5179 5739 7159 7539 9157 9537
1395 1793 3195 3791 5193 5791 7193 7591 9173 9571
1397 1795 3197 3795 5197 5793 7195 7593 9175 9573
1537 1935 3517 3915 5317 5913 7315 7913 9315 9713
1539 1937 3519 3917 5319 5917 7319 7915 9317 9715
1573 1953 3571 3951 5371 5931 7351 7931 9351 9731
1579 1957 3579 3957 5379 5937 7359 7935 9357 9735
1593 1973 3591 3971 5391 5971 7391 7951 9371 9751
1597 1975 3597 3975 5397 5973 7395 7953 9375 9753
39984 86652 133,320 179,988 226,656 = 666,600

Posted 153 day ago

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math_fanatic

Now, I see matherapist's answer. Our answers do agree after I fixed my calculation of 125*25.

The way he added up his final numbers seems simpler than the way I did it, and even though he is a math teacher, he has never seen this problem before. He also gave the first right answer.

My first answer was wrong because of a calculation error. I caught it and fixed it. The only thing I have to say for my answer is that it seems more detailed in its explanation.

I leave it to Raj to determine who the winner is. I doubt he'll get better (and honest) answers in the next two weeks. I say he gives us each $10 and calls it a day. :)

Posted 153 day ago

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math_fanatic

*note - I realized I made a calculation error when I multiplied 125 * 25 the first time so I have reposted my answer with what I believe are the correct numbers.

I am going to answer this even though I see there are 3 other answers. I have not looked at any of the other solutions though.

a) This is the easy part. This is a permutations problem with repetition which is given by the formula n^r where, in this case, n is the number of digits to choose from and r is the number of digits allowed for each number. In this case, n = 5 and r = 4 so n^r = 5^4 = 625. There are 625 different 4-digit numbers using only 1, 3, 5, 7, and 9.

b) By looking at similar, simpler examples where I lined up 2 digit and 3 digit numbers to be summed in columns (1's, 10's, 100's, etc.), I've created a generalized formula for the number of occurrences of each digit per column.

There are n^(r-1) of each digit per column. In this case there are 5^3 (or 125) instances of each digit per column.

The sum of each column in this case is given by 125(1 + 3 + 5 + 7 + 9) = 125 (25) = 3,125

The 1's column adds to 3,125 so the 1's digit of the sum is 5.
The 10's column adds to 3,125 but you've carried over the 312 so you get a sum of 3,437.
The 10's digit is 7.
The 100's column adds to 3,125 but you've carried the 343 so you get a sum of 3,468.
The 100's digit is 8.
The 1000's column adds to 3,125 but you've carried over the 346 so you get a sum of 3,471.

The sum of all the 4-digit numbers with the digits, 1,3,5,7,9 is 3,471,875.

If on the off chance I'm the first person to come up with this solution, my email address is autotheist@gmail.com

Posted 153 day ago

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I have to wait two weeks to see the best correct and detailed answer, and then I have to send a check to the winner. If the winner wishes to donate $20.00 to the charity of his/her choice, I am not concerned. rajbaba78.

Posted 153 day ago

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matherapist

Math fanatic. Your logic seems right but check your multiplication of 125 x 25.I think our solutions will agree. It's a bit different if you do it without replacemnt, but the theory is the same.

Posted 153 day ago

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math_fanatic

I am going to answer this even though I see there are 3 other answers. I have not looked at any of the other solutions though.

a) This is the easy part. This is a permutations problem with repetition which is given by the formula n^r where, in this case, n is the number of digits to choose from and r is the number of digits allowed for each number. In this case, n = 5 and r = 4 so n^r = 5^4 = 625. There are 625 different 4-digit numbers using only 1, 3, 5, 7, and 9.

b) By looking at similar, simpler examples where I lined up 2 digit and 3 digit numbers to be summed in columns (1's, 10's, 100's, etc.), I've created a generalized formula for the number of occurrences of each digit per column.

There are n^(r-1) of each digit per column. In this case there are 5^3 (or 125) instances of each digit per column.

The sum of each column in this case is given by 125(1 + 3 + 5 + 7 + 9) = 125 (25) = 625

The 1's column adds to 625 so the 1's digit of the sum is 5.
The 10's column adds to 625 but you've carried over the 62 so you get a sum of 687. The 10's digit is 7.
The 100's column adds to 625 but you've carried the 68 so you get a sum of 693. The 100's digit is 3.
The 1000's column adds to 625 but you've carried over the 69 so you get a sum of 694.

The sum of all the 4-digit numbers with the digits, 1,3,5,7,9 is 694,375.

If on the off chance I'm the first person to come up with this solution, my email address is autotheist@gmail.com

Posted 153 day ago

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matherapist

First I will say I have never seen this one before. If my answer is correct, please donate the $20.00 to your local animal shelter of favorite charity. If I'm wrong, so be it.

Part 1: with replacement, there are 5 choices for each digit. thus 5*4 = 625 is the number of possible numbers.

Part 2. Each of the columns will have 125 1's 125 3's, 125 5's, 125 7's, and 125 9's

Thus each column will have a sum equal to 125(1+3+5+7+9) or 125*25 = 3125.
If we add the appropriate number of zero's for the 10's 100's and 1000's columns, we get

3125+31250+312500+3125000= 3471875 for the sum

Posted 153 day ago

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matherapist asked 4 digits with or without replacement. I edited the question. rajbaba78

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matherapist

Are you forming 4 digit numbers with or without replacement?

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matherapist	Best Answer First I will say I have never seen this one before. If my answer is correct, please donate the $20.00 to your local animal shelter of favorite charity. If I'm wrong, so be it. Part 1: with replacement, there are 5 choices for each digit. thus 54 = 625 is the number of possible numbers. Part 2. Each of the columns will have 125 1's 125 3's, 125 5's, 125 7's, and 125 9's Thus each column will have a sum equal to 125(1+3+5+7+9) or 12525 = 3125. If we add the appropriate number of zero's for the 10's 100's and 1000's columns, we get 3125+31250+312500+3125000= 3471875 for the sum Posted 153 day ago ( 0 ) ( 0 ) Report Abuse