1. ## brain teaser

I liked the heated up conversation we had about 'sinners and 7 days', so here's a little brain teaser of my own...

You want to measure the weight of any object between 1 and 40 pounds [1, 2, 3, ...39, 40, integers]. you're given a balance scale and you have to choose 4 weights to use. What would they be?

one more thing, if you've seen this before, please PM me instead of just giving out the answer

2. Well, just to spice things up for your brain teaser, I shall volunteer to be wrong again. As soon as I read this problem I thought: binary counting system. This is because you either have the weight or you don't (on or off).

To have the scale read 1, the only weight that works is a 1lb one. Thus 1 must be one of four answers. (In my own mind anyway.) In fact the same logic follows for each power of two just like in binary counting. For 2lb must have 2lb, then three is covered because you have 1+2.....

However this only gives us up to 15 pounds, not nearly the 40 so I'm way off. My guess is that the solution has to do with the fact that it is a balance scale, but maybe this is one for jasrajva (for I really ought to get back to work)..

3. Hey, I tried to PM you but can't ge tthe name into the recepient box right.. what's with the box (the weird character?)

4. eh? Box? I clicked my PM button and it worked for me... emailpikeknightataol.com

5. By four weights do you mean four different degrees of heaviness (allowed more than one of each)... or four weights in total?

If its a balanced scale there is probably a combination of four different weights you can add to each side to make any number - 1 thru 40... I'll have to think about it. If this is the right track though, I think I'll need a limit, otherwise I'll just take 40 * 1 pound weights

6. you get 4 weights (4 objects with masses of integer values). You get to pick what they are.

Ex. 1, 2, 3, 4

or

1, 10, 20, 40

etc.

You have to use these to weigh objects from 1 to 40 kg on a balance scale (the masses of the objects go 1, 2, 3, 4, 5... 40)

I hope that clears it up

7. Are we definately measuring integer masses\weights?
How many measurements are we allowed to make to tell you the weight of things?

8. my cat's name's Mittens.

(you all know you love Ralph.

3^0 = 1
3^1 = 3
3^2 = 9
3^3 = 27

1
3 -1 = 2
3 =3
3 +1 = 4
9 - 3 -1 = 5
9 - 3 = 6
9 + 1 - 3 = 7
9 - 1 = 8
9
9 + 1 = 10
9 + 3 - 1 = 11
9 + 3 = 12
9 + 3 +1 = 13

27 - 9 - 3 - 1 = 14
27 - 9 - 3 =15
27 - 9 - 3 +1 = 16

27 - 9 - 1 = 17
27 - 9 = 18
27 - 9 +1 =19
27 - 9 + 3 - 1 = 20
27 - 9 + 3 = 21
27 - 9 + 3 +1 = 22
27 - 3 - 1 = 23
27 - 3 = 24
27 - 3 + 1 = 25
27 - 1 = 26
27

and so on

im too bored to write the whole thing out

Justin was partially correct abt the binary logic
if we are only alloewd to add the weights then to measure all weights from 1 to x

we need 2^0 , 2^ 1, 2^2, .... till 2^n where

2^n < x < 2^(n+1)

but if we can both add and subtract(ie place weights on either side of the balance then we need

3^0 , 3^ 1, 3^2, .... till 3^n where

3^n < x < 3^(n+1)

i know a friend who has proved this but couldnt find him today

no i didnt know the answer i just got it by chance when i was trying to figure out the same for 1..10 with three weights

though i suspect there mite be more answers to this as if the problem is

to measure 1..10 with three weights the choices are many

1,3,9
1,2,8
1,3,7
....
.etc

ill try to prove the 3^n result tell me if anyone of you gets it first

jv

10. good job!

I'm still trying to figure out if there are any other possibilities besides the base 3 weights....

11. Ah yes, a balance scale. The weight can be on side A, B, or not placed on the scale at all. That looks like three states to me. Base 3 it is then. 1+3+9+27 = 40. Given the rules of base, all answers less than 40 to 0 are covered.