Lateral Thinking Math Problem- Tough!!

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Hello,

I was recently reading a lateral thinking book, and I came about this problem. I’ve been racking my brain trying to figure it out. Here is the problem

There are two glasses of equal size, glass A and B. A is empty and B contains some water. Half of glass B is poured into A. Once again, half of what is in B is poured into A. Once more, half of glass B is poured into glass A. At the end of 3 pourings, A is half full. How much water is left in B?'

Here is what I have so far...

Say X is the original amount of water in glass B

1/2X + 1/4X + 1/8X = 7/8 X

You see, however much water was in glass B to start, half is left after one pouring, a quarter is left after the second pouring and an eighth is left after the third pouring. So seven eights has been transferred.

..BUT WHAT DO I DO KNOW?? Please help me solve this sucker, and please show your steps algebraically (as best you can) and provide reasoning. Thanks!!

-Ryan
 
Maybe I am misconstrued, but this seems like one of those 'red herring'

problems. Sort of like the lost dollar.

We don't know the full capacity of the glasses.

The fact that 'glass A is half full' is immaterial, isn' t it?. Glass B still has

1/8th left. You poured out 7/8th of what was in it.
 
Well...

1/2X + 1/4X + 1/8X = 7/8X
So 7/8X = 1/2 a glass

All that water that was added into cup A equals 7/8thsX. And since A is half full, 7/8X equals half a glass.

But i'm not sure where to go from there. Any other ideas?
 
7X / 8 = 1/2 glass, so glass = 7X / 4

Left in B is X/8; (X/8) / (7X/4) = 1/16 of glass :shock: :idea: :?:
 
Anytime I see 'lateral thinking' I think tricky. Maybe not. 7/8th of the water poured from B is equal to 1/2 B's total capacity(since it's the same size as A).

I thought maybe this was like the eggs and the basket.

If there are 6 eggs in a basket and 6 people each take 1 egg, why is there 1 egg left in the basket?.

Because the last person picked up the basket with the last egg in it.

Rather obvious, but alot of times one doesn't think of it because the brain is trained a certain way. One may picture each person taking an egg out of the basket.
 
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