A Question Of Weight

[TheGoodGuy]

It all seems to be gathering dust here in the Trivia zone doesn't it?

Oh well,

Have a go at this.....not mind-bendingly difficult, but something to restart the interest, hopefully!!

Next door neighbour farmers Giles & Brown were off to market to sell their produce to the locals.
They met en route, with Farmer Giles in his wagon laden with his produce to sell and dozens of weights to measure out his goods at the market, and Farmer Brown in his wagon also laden with goods to sell but with just 4 pairs of weights to measure out his wares.
"Why so many weights" asked Farmer Brown to Farmer Giles, "I only need a pair each of four different weights to measure any quantity from 1kg to 170kg".

What are the 4 weights Farmer Brown needs to have to verify his claim?

Ada.

[TheOldhamWhisper]

I haven't worked out every combination, but I think two each of 11, 20, 25 and 29 should cover it.

[TheGoodGuy]

Oldham,

It's not the answer I've got....

Explain how you would measure say...1kg or 8kg.
I daresay you can do it, I just need clarification to verify your answer.

Ada.

[TheOldhamWhisper]

1kg = 2*25 on one side with 1*20 and 1*29 on the other
8kg = 2*29 on one and 2*25 on the other

As I said, I haven't worked them out, so I'd be happy for someone to find a weight that cannot be found.

[stevesouth]

can you do 147KG ??

[TheOldhamWhisper]

147kg could be achieved by first weighing out 23kg of (wrapped) produce (25 and 20 one side 2*11 on the other). Then, placing all the weights on one side (170kg) and the (wrapped) weighed produce on the other, add to the scales til they balance. The added goods will weigh 147kg.

[John]

1kg = 2*25 on one side with 1*20 and 1*29 on the other

Wouldn't that give you 1kg?

I'm a bit flummoxed with this thread... basically are we looking for 4 weights that when combo'd together can measure any number between 1 and 170?

[TheOldhamWhisper]

Yes John - but it is 4 pairs of weights (eight in total).

[GlosRFC]

Saw this late last night so haven't given it too much thought other than prime or Fibonacci numbers might be useful. But one thought that did cross my mind is that, depending on the wares farmer Brown is selling, it's possibly to way any quantity between 1kg and infinity using a 1kg weight. So if he's selling grain, and a customer asks for 15kg, all he needs do is weigh out 15 times 1kg portions. Alternatively he can employ a similar method to the one that Oldham suggests:-
1. Weigh out 1kg of grain on left hand scales.
2. Place this grain right hand scales with 1kg weight and weigh out 2kg.
3. Place this grain on right hand scales and weigh out 4kg.
4. Place this grain on right hand scales and weigh out 8kg.

Ergo, 15kgs of grain weighed out in just four steps. I know it's not the solution that Ada is looking for but it seems perfectly acceptable to me :D

[TheGoodGuy]

Once again what I thought to be a fairly taxing but straightforward puzzler has resulted in excellent & what appear to be correct variations of the answer I was expecting (sorry....hoping for).

Well done... but...

The answer I WAS expecting (& to me seems the most logical):

A pair of each: 1kg, 4kg, 16kg, 64kg.

Ada.

[TheOldhamWhisper]

I'll go with your answer Ada - should have been easy enough to work out (but they always are once you know the answer!) :)