# Can you guarantee that if you have a group of five numbers you can pick out three that will add up to a multiple of 3?

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Yes. Here's why...

What we need to do is find five numbers out of which a combination of three can not be picked whose sum is divisible by three.

The easiest way to see whether or not that's possible is to look at all possible numbers as sets, grouped by their offsets from multiples of three. That gives us three sets:

a(x) = 3x + 0 = {0, 3, 6, 9, 12, 15, 18, 21, 24 ... }
b(x) = 3x + 1 = {1, 4, 7, 10, 13, 16, 19, 22, 25, ... }
c(x) = 3x + 2 = {2, 5, 8, 11, 14, 17, 20, 23, 26, ...}

There are two important things to note here:

1) First, any three numbers selected from one of those sets will add up to a multiple of three. This can be demonstrated very easily. Let's take set C. We'll pick three random numbers out of the selection, calling them x, y, and z. Their sum then would be:

3x + 2 + 3y + 2 + 3z + 2
= 3x + 3y + 3z + 6
= 3(x + y + z + 2)
which means that all possible selections will be a multiple of three. Now let's try that with set B:

3x + 1 + 3y + 1 + 3z + 1
= 3(x + y + z + 1)
again, all answers are multiples of three.

This is most obvious with set A, where the results would be expressed simply as:
3x + 3y + 3z
= 3(x + y + z)

This means that in order for our set of five numbers to meet the conditions we want, no more than two can be picked out of any of those three sets.

2) The second important note to look at is that if we pick a random number out of each of those sets, and add them together, they too will add up to a multiple of three. Here's the proof, again with our three random selections of (x, y, z):

a(x) + b(y) + c(z)
= 3x + 0 + 3y + 1 + 3z + 2
= 3x + 3y + 3z + 3
= 3(x + y + z + 1)

This means that we can't pick a number out of all three sets. Otherwise, a sum that's divisible by three can be found.

Now consider these facts together:
1. we have three sets that include every possible number that we can select
2. we can pick at most two numbers out of each of those sets
3. we can pick numbers out of at most two of those sets

These conditions can not be met if we want to pick five numbers. We can find four that meet this condition (a pair out of any two of the sets), but if we want to pick a fifth one, it must either come from the third set, breaking our limit of two sets, or from one of the ones we've already picked from, breaking our limit of two per set.
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# What 3 numbers add up to 11?

Assuming all numbers are to be greater than zero and no duplicates exist within each possible answer, there are 5 possible combinations:. 1 + 2 + 8, 1 + 3 + 7, 1 + 4 + 6, 2 + 3 + 6, and 2 + 4 + 5.. If one number is allowed to be zero and no duplicates exist within each possible answer, there are 5 (MORE)

# What three prime numbers add up to 100?

{ 2, 19, 79 } { 2, 31, 67 } { 2, 37, 61 }

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no because first of all you should have said different positive whole #s because now i can say 1*1*1=1 which is not a multiple of 3 but assuming they are different it is still a no because 2*1*5=10 which is not a multiple of 3

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No 17 + 3 = 20 2 + 19 = 21 20 + 21 = 41 41 + 5 = 46

# What five odd numbers add up to 100?

No 5 odd numbers add up to 100. The sum of any two odd numbers is even. The sum of any two even numbers is even. So the sum of any 4 odd numbers must be even. Take that and add an odd number and the sum must be odd. Therefore, the sum of any 5 odd numbers must be odd. 100 is even. In c (MORE)

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41 -- Less than 100 -- 42 is the multiple of 7 -- 4 + 1 = 5

# In which group are all three numbers multiples of 35?

I can't tell. I can't see the groups clearly from here, mainly because you're keeping them hidden.

# WHAT number is a 2 digit number a multiple of both 3 and 4 and the sum of its digits add up to 15?

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# What 3 numbers add up to 24?

This has an infinite number of solutions; choose any two numbers for your first two numbers, then solve for the third.\n This has an infinite number of solutions; choose any two numbers for your first two numbers, then solve for the third.\n This has an infinite number of solutions; choose any two (MORE)

# How do you draw two straight lines on a clock to make three groups of four numbers to add up twenty-six?

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# What three consecutive numbers add up to forty two?

Let the numbers be a - 1, a and a+1. Adding we get 42. This means a-1+a+a+1 = 42 ie 3a = 42 Therefore, a =42/3 = 14. Hence the consecutive numbers are 13,14 and 15. you check yourself by adding these.

# What 3 numbers add up to 51?

Several groups of 3 numbers add up to 51 Here are some: 30 + 20 + 1 = 51 15 + 30 + 6 = 51 ===== Another contributor added: Actually, there are an infinite number of possibilities. Here are a few more. 16 + 17 + 18 16.9 + 17 + 17.1 16.00009 + 17 + 17.99991 0.1 + 0.2 + 50 (MORE)

# Three consecutive numbers that add up to a multiple of three?

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# What are the three most drawn Pick 3 numbers?

If, over a long period of time, any numbers are drawn any more or less often than any other numbers, then the game is a fraud and would be shut down. The states that run lotteries pay accounting firms big bucks to keep track of this.

# What are the three even numbers add up to 54?

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# What numbers are multiples of 3 up to 1000?

3. 6. 9. 12. 15. 18. 21. 24. 27. 30. 33. 36. 39. 42. 45. 48. 51. 54. 57. 60. 63. 66. 69. 72. 75. 78. 81. 84. 87. 90. 93. 96. 99. 102. 105. 108. 111. 114. 117. 120. 123. 126. 129. 132. 135. 138. 141. 144. 147. 150. 153. 156. 159. 162. 165. 168. (MORE)

# What are three consecutive numbers that add up to 15?

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# What are three even numbers add up to 2658?

We suspect that there are thousands of correct answers to this one. Here's one: 2, 4, 2652. If the question intended to ask for three consecutive even numbers but suffered from lack of proofreading, those would be 884, 886, 888 .

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There is an infinite list of correct solutions. Here are a few: 1 + 2 + 73 21 + 19 + 36 -9.724 + 4.019 + 81.705

# What 3 numbers add up to 600?

Algebraically. X = numbers. X + (X + 1) + (X + 2) = 600 3X + 3 = 600 3X = 597 X = 199 199 + 200 + 201 = 600

# What three consecutive even numbers add up to 456?

150, 152, 154 . Let the three consecutive even numbers be 2n-2, 2n & 2n+2, then: (2n-2) + 2n + (2n+2) = 456 Ã¢Â‡Â’ 6n = 456 Ã¢Â‡Â’ n = 76 Which means the three numbers are: . 2n-2 = 2 x 76 - 2 = 150 . 2n = 2 x 76 = 152 . 2n+2 = 2 x 76 + 2 = 154

# What five consecutive numbers add up to 505?

We can calculate this by saying: x + x + 1 + x + 2 + x + 3 + x + 4 = 505 We simplify this to: 5x + 10 = 505 5x = 505 - 10 5x = 495 x = 99 Thus the answer is: 99,100,101,102 & 103.

# What are all the combinations of three numbers that add up to thirteen?

It will depend on wether you can use 0 and if a number can be repeated but assuming that you can only use each digit once in the equation and that you can count 0 as one of them, your answer would be as follows: 0,1,12 0,2,11 0,3,10 0,4,9 0,5,8 0,6,7 1,2,10 1,3,9 1,4,8 1,5,7 2,3,8 2,4,7 2,5,6 3,4,6

# What are three numbers add up to 50?

Do they have to be all the same numbers? If not, you're a retard if you don't know that! (: just kiddin. I love you!

# What is the number this is a multiple of five and three and has eight factors?

There are an infinite number of numbers that are a multiple of 3 & 5 and have [exactly] 8 factors. The lowest is 30. The next few are: 105, 135, 165, 195, 255, 285, 375, 435, ... . Any number of the form 15p where p is a prime number (which is 2 or greater than 5) will be a multiple of 3 & 5 a (MORE)

# What five consecutive numbers add up to 225?

Call these five numbers x,y,z,a, and b. We know that x = y+1 = z+2 = a+3 = b+4 so 225 = x + x + x + x +x - 1 - 2 - 3 - 4 235 = 5x x = 47, so the five numbers are 43,44,45,46,47.

# What three numbers add up to a prime number?

if you mean what three prime numbers add up to a prime number then the answer is : 5 + 7 + 11 = 23

# What numbers multiple to 400 and add up to -50?

-10 and -40 multiply to 400 (because the negative signs cancel each other) and add to -50. Please note that WikiAnswers is not here to do your homework for you. If this question is from work you have been assigned by a teacher or professor, I suggest you do the work yourself instead, which will hel (MORE)

# What three consecutive numbers add up to 25?

That isn't possible. The three consecutive number are assumed to be integers; the sum of three consecutive integers is always a multiple of 3 (try it out).

# How do five threes add up to 100?

They don't. Five threes add up to 15 and that is it! You can write an expression using 5 threes that makes 100, but that is not the same.

# How many ways can three numbers add up to eleven?

There is an infinite number of ways three numbers can have the sum of 11

# What three consecutive numbers add up to twenty?

There are no three consecutive numbers that add up to twenty. Proof: 5+6+7=18 6+7+8=21 7+8+9 = 24

# What three prime numbers add up to 59?

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 are the numbers you have to work with. So 53 + 5 + 1 = 59 but 1 isn't a prime. But 47 + 7 + 5 = 59 and 41 + 11 + 7 = 59 and if you allow duplicates 37 + 11 + 11 = 59 and so forth.

# What are the three prime numbers that add up to 13?

You can find this out quickly, if you just experiment a bit. There are actually two solutions: 5 + 5 + 3 7 + 3 + 3

# What five odd numbers add up to twenty-one?

Several solutions. 17 + 1 + 1 + 1 + 1 15 + 3 + 1 + 1 + 1 13 + 5 + 1 + 1 + 1, 13 + 3 + 3 + 1 + 1 11 + 7 + 1 + 1 + 1, 11 + 5 + 3 + 1 + 1, 11 + 3 + 3 + 3 + 1 9 + 9 + 1 + 1 + 1, 9 + 7 + 3 + 1 + 1, 9 + 5 + 5 + 1 + 1, 9 + 5 + 3 + 3 + 1 7 + 7 + 5 + 1 + 1, 7 + 7 + 3 + 3 + 1, 7 + 5 + 5 + 3 + 1, (MORE)

# What 3 numbers add up to 4.438?

There are infinitely many sets of 3, A relatively easy set to work out is 4 0.4 and 0.038

# What 3 numbers add up to 92?

Start with 1, 2 as the first two numbers. Subtract those numbers from the original number. The remaining number is one possible outcome. Dont be a dingus next time.

# What are three consecutive numbers that add up to 93?

93 / 3 = 31 so 31 is the middle number 30 + 31 + 32 = 93

# What three numbers add up to 100?

There are infinitely many possible answers. One such is -50, 250 and -100. Another 33, 33 and 34.

# How many three digit numbers add up to 22?

Infinitely many triples do. For example, (100, 100, -178) (100, 101, -179) (100, 102, -180)

# What three prime numbers add up to 66?

it is 61 + 2 + 3 because if you add 61 + 5 it = 66so if you split 5 into 2 and 3 it = 5 then add 61 to 5 and you get66

# What two numbers add up to -20 but multiple -60?

The numbers are: 2.649110641 and -22.629110641 A more accurate answer can be found by using the quadratic equation formula

# What three multiples add up to get 42?

Multiples don't add. Addends add, like 13 + 14 + 15 = 42 but I suspect you want factors,specifically prime factors. 2 x 3 x 7 = 42

# What number multiples to 90 but adds up to -45?

The factor pairs of 90 are (90,1)(45,2)(30,3)(18,5)(15,6)(10,9) Even considering their negative counterparts, none of them add up to -45 Another Answer:- The numbers are: -2.097794237 and -42.902205763

# What three consecutive numbers add up to 504?

504 / 3 = 168 then add 1 on and take 1 off so 167 + 168 + 169 = 504

# Three of the following numbers add up to the number 31 17 3 2 19 5.?

If you can only add some or all of the numbers together - youcannot achieve a total of 31. You can get the total 31 bythe following... (19-2) + 17 - 3

# What are three consecutive numbers that add up to 255?

84, 85, 86 x+x+1 + x+2 = 255 3x = 255 -1-2 =252 x = 252/3 = 84 therefore x + (x+1) + (x+2) = 84+ 85 + 86

# What 3 numbers add up to 12?

3 + 4 + 5 many answers 1 + 1 + 10 2 + 6 + 4 8 + 1 + 3 and so on ...