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# Alex's 55-pint Birthday Bonanza

## Question

Happy Birthday to me ... HBTM ... etc sang Alex as he strolled into Morty's

last night and then announced, Boys, I've got a real treat for ya tonight!

First, take a look at this. And he hung from the ceiling a complicated,

interconnected set of five scales, whose 10 balance pans he'd labeled

A, B, C, ... H, I, J.

Now the barkeep gave me one request, bein' it's my birthday on Saturday, and all.

He's gonna draw out fifty-five cold pints. Then, if we can place a different number

of pints into each of these balance pans, we'll have a real party, cuz the drinks

will be on the house!

Every pan gets a pint to start with, and all five scales have to balance.

Alright boys, let's get at it ... we have until midnight to get this done.

Otherwise we pay for the drinks.

Feel free to help Alex, Jamie, Davey and the boys celebrate!

Edit for clarity

The marks on the bars are equally spaced.

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ok.

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I think there might be an error here. A lever exerts the force of pressure times length. So J will weigh 8J. H-I will weigh 2(H+I) and E+F+G must = A+B+C+D. Also, A+B+C+D+E+F+G must = 1/2 of 8J+2(H+I). IF this is true, then A+B+C+D and E+F+G must both be fractions.

8J+(2(H+I)). Must be even if J, H, and I are whole numbers. Therefore A+B+C+D and E+F+G must both be odd. Odd+odd =even. Therefore if A+B+C+D and E+F+G are equal and 1/2 of an odd number, they must be a fraction. Right

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A+B+C+D+E+F+G must = 1/2 of 8J+2(H+I). = 4J + (H+I)

IF this is true, then A+B+C+D and E+F+G must both be fractions Right?

They're not half of an odd number if If H and I are both odd or both even.

Then 4J + [H+I] is even, and (A+B+C+D) and (E+F+G) are each half of an even number.

Now put [H and I are both odd or both even] together with 3H=2I and you're well on your way.

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Yeah, I get you. I was really close but messed up by leaving 1/2 of the left hand weight off when I tested H and I for what they need to be. Let me give it another shot.

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Yeah, EZ when I don't muff my math.

A=2

B=5

C=3

D=9

E=1

F=8

G=10

H=6

I=4

J=7

Hmmm. 11:00 PM - LET'S PARTY!

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AS a P.S. - I'd love to see this beer mobile hanging from a bar ceiling!

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So a pint weighs about a pound and a tenth. If you assume a force of 3 pints will upset the balance enough to spill all the drinks, how do you get the pints down to drink them?

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So a pint weighs about a pound and a tenth. If you assume a force of 3 pints will upset the balance enough to spill all the drinks, how do you get the pints down to drink them?
Get Alex, Jamie and Davie to remove 2 or 3 glasses at a time,

keeping things balanced at each step.

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