Quantitative reasoning problem

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The discussion centers on the ability to create any number using a construction rule based on a limited set of numbers, specifically citing the example of producing the number 87 from the numbers 1, 2, and 3. Participants express confusion over the validity and clarity of the construction rules provided, questioning the lack of unambiguous answers. There is a consensus that the exercise may lack meaningfulness without a clear explanation of the rules applied. The thread concludes with a decision to close the discussion due to insufficient contributions from the original poster. Overall, the conversation highlights the complexities and ambiguities in quantitative reasoning exercises.
Chijioke
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Homework Statement
Study the examples and use it to find the missing numbers.
Relevant Equations
If the relationship in the examples can be deduced, looking for the missing numbers would not be a problem.
IMG_20231104_112510.jpg
 
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You can find a construction rule for any number. There are no unambiguous answers. Example:

1699189441157.png


Answer: ##87##
Reason: ##.\overline{1}^{-2}+3!=87##
 
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fresh_42 said:
You can find a construction rule for any number. There are no unambiguous answers. Example:

View attachment 334861

Answer: ##87##
Reason: ##.\overline{1}^{-2}+3!=87##
I don't understand.
 
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Chijioke said:
I don't understand.
I gave you an example how to produce the number ##87## by a construction rule that only used the three numbers ##\{1,2,3\}.## Isn't that absurd? You can create a lot of numbers from three given ones.

There is either an explanation about that specific arrangement with four numbers that you haven't told us or it is a worthless and meaningless exercise. You could write down any number in the empty fields and construct a rule afterward.
 
It has to be the same one rule for the three examples on top, I guess. Then the same rule should be applied in the other twelve.
 
Hill said:
It has to be the same one rule for the three examples on top, I guess. Then the same rule should be applied in the other twelve.
Before we keep guessing, and with respect to the fact that the OP didn't try to help himself or us, I will close this thread.
 
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Thread 'Find the polar form of a complex number'

The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.
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