What is the Pattern for Finding the Missing Number in a Sequence?

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SUMMARY

The discussion focuses on identifying patterns for finding missing numbers in sequences, specifically through the use of multiplication and addition. A participant successfully deduced that for the number 28, the factors 4 and 7 correspond to the sums of pairs (1+3) and (5+2), leading to the equation 4 * 7 = 28. This method demonstrates a systematic approach rather than random guessing, emphasizing the importance of recognizing additive relationships in sequences.

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Homework Statement
what's the missing number
Relevant Equations
nothing comes to mind
I have no idea. I've tried squaring, cubing, summing numbers but can't make sense of anything. Literally no clue how to even approach this aside from randomly adding and subtracting numbers, their squares and cubes, but nothing makes sense. Any ideas?

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fresh_42 said:
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But how? And how would I even go about doing this?
 
28=4*7=(1+3)*(5+2)
 
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anuttarasammyak said:
28=4*7=(1+3)*(5+2)
How on Earth did you know to do this? Just random guessing? What all did you check prior to this?
 
joshmccraney said:
Just random guessing?
Not really. The very first thing I tried, for all of about 5 seconds, was addition, which seemed a dead end. Then I noticed that in the first problem 5 and 2 added to 7, and 3 and 1 added to 4 -- 4 * 7 = 28. The pattern was the same for the second problem.
 
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Mark44 said:
Not really. The very first thing I tried, for all of about 5 seconds, was addition, which seemed a dead end. Then I noticed that in the first problem 5 and 2 added to 7, and 3 and 1 added to 4 -- 4 * 7 = 28. The pattern was the same for the second problem.
Makes sense, thanks.
 

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