Pure maths, physics, chemistry, etc.: brain-training tasks that have nothing to do with trade [Part 2] - page 37

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Here's another interesting problem. A third-grade daughter also gave it to me.

What four weights can be used to weigh any weight from 1 to 40 grams (inclusive). Fractional, of course, does not count. Weights can be placed on both sides of the scale.

 
shredder:
1 3 9 27
 
Quickly :) I've probably met the task before.
 
shredder:

That's right! The problem has 62 correct solutions, and this is one of them :)

Give me another five or ten solutions. I don't think so. Not that there aren't more solutions, but that's too many. :)
// but if you allow brackets (priorities), then I believe you.

 
shredder:
Quickly :) Probably met the task before.
There was something, yes.
 
MetaDriver:

not that there aren't more solutions, but that's a lot of what you said. :)
// but if brackets (priorities) are allowed, then I believe you.


Why not:

1+2+3+4-5-6*7+8 = 1

1+2+3+4*5+6/7/8 = 1

1+2+3-4+5-6+7/8 = 1

1+2+3-4*5+6-7-8 = 1

1+2-3+4+5+6-7/8 = 1

1+2-3-4*5+6+7+8 = 1

1+2-3*4+5-6*7+8 = 1

1+2-3*4-5+6+7/8 = 1

1+2-3*4*5*6-7+8 = 1

1+2-3*4*5/6-7+8 = 1

1+2-3*4/5*6-7+8 = 1

1+2-3*4/5/6-7+8 = 1

1+2-3/4+5-6*7+8 = 1

1+2-3/4-5+6+7/8 = 1

1+2-3/4*5*6-7+8 = 1

1+2-3/4*5/6-7+8 = 1

1+2-3/4/5*6-7+8 = 1

1+2-3/4/5/6-7+8 = 1

1+2*3+4-5-6+7-8 = 1

1+2*3-4+5+6-7-8 = 1

1+2*3-4-5*6-7+8 = 1

1+2*3-4-5/6-7+8 = 1

1+2/3+4+5+6-7-8 = 1

1+2/3+4-5*6-7+8 = 1

1+2/3+4-5/6-7+8 = 1

1+2/3-4-5-6+7+8 = 1

1+2/3*4+5+6-7/8 = 1

1+2/3/4+5/6/7*8 = 1

1-2+3-4-5+6*7+8 = 1

1-2+3/4*5*6-7/8 = 1

1-2-3+4+5-6*7+8 = 1

1-2-3+4-5+6+7/8 = 1

1-2-3+4*5*6-7+8 = 1

1-2-3+4*5/6-7+8 = 1

1-2-3+4/5*6-7+8 = 1

1-2-3+4/5/6-7+8 = 1

1-2-3/4-5+6-7+8 = 1

1-2-3/4-5/6*7+8 = 1

1-2-3/4*5+6+7/8 = 1

1-2*3+4+5-6-7+8 = 1

1-2*3+4+5/6+7/8 = 1

1-2*3+4-5+6+7-8 = 1

1-2*3+4*5-6*7+8 = 1

1-2*3*4+5+6*7+8 = 1

1*2+3-4+5-6-7+8 = 1

1*2+3-4+5/6+7/8 = 1

1*2+3-4-5+6+7-8 = 1

1*2+3-4*5-6*7+8 = 1

1*2-3+4+5-6+7-8 = 1

1*2-3-4+5*6-7+8 = 1

1*2-3-4+5/6-7+8 = 1

1*2-3*4*5+6+7+8 = 1

1*2*3+4-5-6*7+8 = 1

1*2*3+4*5+6/7/8 = 1

1*2*3-4+5-6+7/8 = 1

1*2*3-4*5+6-7-8 = 1

1*2/3*4-5*6+7+8 = 1

1/2+3+4-5*6-7/8 = 1

1/2+3*4-5+6-7/8 = 1

1/2-3*4+5+6+7/8 = 1

1/2*3+4+5*6/7-8 = 1

1/2*3-4+5*6-7/8 = 1

count = 62

 
shredder:


Why not give: ...........

count = 62

Yep, score. Checked a few things randomly - it all adds up. :)
 
MetaDriver:
Yep, it checks out. Checked a few things on a random basis - it all fits. :)
You're tough, but you're fair!
 
tara:
You are strict but fair!
Why the sudden name-calling? :)
 
MetaDriver:
Yep, it checks out. Checked a few things on a random basis - it all fits. :)

I did it with a script, so it should work :) Although I did a little spot-checking myself, too.
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