## Word problems in the form: a is to b as c is to d

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quarkcosh1
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### Word problems in the form: a is to b as c is to d

Where the variables are words. I remember seeing problems in this form on the SAT when I took it years ago. Does anyone know what these types of problems are called? Also I thought of some problems relating to them:

1. How many possible values for the variables are there?
2. Find values for a and b so that there are no solutions to c and d?
3. Find values for a and c so that there are no solutions to b and d?

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### Re: Word problems in the form: a is to b as c is to d

I think they're just called analogies, or analogy questions.

Those questions seem ill-defined to me, but I'll take a stab:
1. There's a lower bound at N^2, where N is the number of words (because IMO there's a solution* for every combination of A and B).
2-3. impossible

*For some definition of "solution"...

gmalivuk
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### Re: Word problems in the form: a is to b as c is to d

Yeah, the way these work is that you find some relationship between a and b and transfer that same relationship to c and d. As you (the OP) have demonstrated yourself in that grammar = particle physics thread, it is always super easy to come up with possible relationships.
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Derek
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### Re: Word problems in the form: a is to b as c is to d

Yep, analogies. They were removed from the SAT some years ago.

quarkcosh1
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### Re: Word problems in the form: a is to b as c is to d

I was thinking about another problem where a, b, and c were known but d wasn't (I will write them in the form a:b = c:d). For example using a random word generator I came up with this: spoil:bold = watch:d. You pretty much have to use a random word generator to come up with these otherwise the words are likely to have some connection. Anyway does anyone have some good possible values for d? I really want to try to understand problems like these better due to their connection to creativity.

Deva
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### Re: Word problems in the form: a is to b as c is to d

Spoil (food): bold (smell) = watch (vision): bright (stimulation)
Spoil (plot): bold (behavior) = watch (a show): patient (behavior)

Likens these to Rorschach ink blots and word associations. Stretches to make something fit. (Created another analogy.)
Changes its form depending on the observer.

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### Re: Word problems in the form: a is to b as c is to d

quarkcosh1 wrote:I was thinking about another problem where a, b, and c were known but d wasn't (I will write them in the form a:b = c:d). For example using a random word generator I came up with this: spoil:bold = watch:d. You pretty much have to use a random word generator to come up with these otherwise the words are likely to have some connection. Anyway does anyone have some good possible values for d? I really want to try to understand problems like these better due to their connection to creativity.
Otho or ethe? (relationship between length and common letters)

mathmannix
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### Re: Word problems in the form: a is to b as c is to d

spoil: bold = watch: jewelry customers (?)
spoil: bold = watch: duty officers (?)

(To the bold go the spoils; to the _?_ go the watches)
I hear velociraptor tastes like chicken.

gmalivuk
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### Re: Word problems in the form: a is to b as c is to d

Those are clever.

There's a reason tests with analogies always give multiple choices, and it isn't just because multiple choice tests are easy to check. If you know the meaning of the given words, it's usually pretty straightforward and unambiguous to pick which of four or five options is clearly the best way to complete it. If you don't have a short list of choices, on the other hand, it becomes like those "continue this sequence" number problems, where there are often quite a few reasonable possibilities even if we restrict ourselves to easily expressible generating rules.
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quarkcosh1
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### Re: Word problems in the form: a is to b as c is to d

Wow it takes me a few minutes of staring at these to get them. Lets do some more so I can get better at these.

bottle:mystery = flicker:x
bell:dinosaur = dark:y
knot:cuteness = ghost:z

Deva
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### Re: Word problems in the form: a is to b as c is to d

bottle : mystery = flicker : mechanism
bell : dinosaur = dark : bats (animal)
knot : cuteness = ghost : somber

1. Imagined a mysterious substance inside a bottle. What flickers? Light bulbs. Why is a light bulb flickering? Shrugs. Presumes some unknown, faulty mechanism inside it.

2. Thought of Pavlov's dogs, but with dinosaurs. Who would darkness be a response for? Chose bats.

3. Interpreted it as "tying the knot". Works with cuteness. Paired ghost with funeral (or graveyard). Considers them somber.
Changes its form depending on the observer.