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# help

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The numbers 49, 29, 9, 40, 22, 15, 53, 33, 13, 47 are grouped in pairs so that the sum of each pair is the same. Which number is paired with 15?

Jun 4, 2020

#1
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I found this question in my math packet once too. I dug it up and found it was multiple choice, so just match it up with the answers.

33, 40, 47, 49, 53

Match them and see.

49, 29, 9, 40, 22, 15, 53, 33, 13, 47

Does 53 work? Doesn't match with 49, 29, 9, 40, 22, 53, 33, 13, 47

Does 49 work? Doesn't match with 49, 29,9, 40, 22,53,33, 13, 47

Does 47 work? It matches! Solution found lol.

Yay!

Jun 4, 2020
#2
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53 9

49 13

47 15

40 22

33 29

Jun 4, 2020
edited by Guest  Jun 4, 2020
#3
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The numbers 49, 29, 9, 40, 22, 15, 53, 33, 13, 47 are grouped in pairs so that the sum of each pair is the same. Which number is paired with 15?

The highest number in the list is 53 so all the totals will have to be larger than 53.  I knew it couldn't be a large number paired up with another large number or the other pairs couldn't be that much, so I tried the smallest number, 9.  The total is 62.  So I tried pairing up others to total 62.  That seemed to work okay, and the one that pairs with 15 is 47

.

Jun 4, 2020
#4
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Add them up sequentially, then sort them in numerical order and should get 5 sums in a row that are the same. When you do that, this is the result:
(22, 24, 28, 31, 35, 37, 38, 42, 42, 44, 46, 48, 49, 51, 53, 55, 55, 56, 58, 60, 62, 62, 62, 62, 62, 64, 66, 68, 69, 69, 71, 73, 75, 76, 78, 80, 82, 82, 86, 87, 89, 93, 96, 100, 102)
You can easily see that the 5 numbers are sums of 62. Then, there is no guessing: 62 - 15 =47

Jun 4, 2020