Brain Teaser

chris snell

Administrator
Callsign: NW5W
Staff member
This showed up on Slack at work and it was too good not to share. I saw some pretty amazing solutions to this in the responses. I think the best was around four steps.

Code:
You wanted to split 300 grams salt into three 100g piles with only one balance scale, one 5g weight and one 30g weight.
What is the least steps you can think of finishing this task? And how?
 

LiquidMoose

Well-known member
Forget the weights. Scoop two piles onto the scale until they equal, you are then left with three equal piles. No idea how many steps that would be, but mission accomplished.
 

theShaytoon

Well-known member
Place both weights on the left side of the scale and add enough salt to the right side to balance.
Move the weights to the right side and add salt to the left side to balance
Move the 30g weight to the left side, remove the 5g weight, and add salt to the right side to balance
Remove the 30g weight and add salt to the left side to balance...3 piles of 100g.

PS....No matter what, do not sneeze...and if it is really "salt", don't snort either.
 

chris snell

Administrator
Callsign: NW5W
Staff member
300g
150g = 150g
75g = 75g = 150g
75g + 30g = 100g + 5g
100g = 100g = 100g

Yep, this is the best solution that I've seen. Someone at work proposed this one, too. Another person at work claims a 4-step solution but never posted it.
 

AdamSanta85

Well-known member
I was thinking

35 : (30 weight + 5 weight) x 2 = 70g
30 : 30 weight = 30g + 70g already weight = 100
Weigh 100 against 100

Is that 4 or 5?
 

erover82

Well-known member
I think shaytoon wins this one. That is 4 steps. Erovers I believe is 5. Both nice results.

The problem is that while a = b may be true, it is not equivalent to a = b = c, which one would only reach with many iterations of swapping and balancing.

Example, (expressed in nerd for chris)
107 = 107 != 86
107 != 96.5 = 96.5
101.75 = 101.75 != 96.5
101.75 != 99.125 = 99.125
100.4375 = 100.4375 != 99.125
100.4375 ≈ 99.78125 ≈ 99.78125 ?
 
Last edited:

theShaytoon

Well-known member
I think the concept of "step" has to be defined to get a correct solution... For example a step can be defined as the process to balance the scale. Or it can be defined as add/remove weights...
 

MountainD

Technical Excellence Contributor
The problem is that while a = b may be true, it is not equivalent to a = b = c, which one would only reach with many iterations of swapping and balancing.

Example, (expressed in nerd for chris)
107 = 107 != 86
107 != 96.5 = 96.5
101.75 = 101.75 != 96.5
101.75 != 99.125 = 99.125
100.4375 = 100.4375 != 99.125
100.4375 ≈ 99.78125 ≈ 99.78125 ?
Not true. TheShaytoon was super duper careful. His pile was, to the grain, precisely 300g, and when he measured, his super duper scale was perfect. So when he took out 100g, it was perfect. He almost dropped 1 grain of sand when his dog farted, but he found it and put it back in the right pile. His measuring skillz are legendary. Shaytoon scales are still used throughout Switzerland and are prized tools. His family has been in scales weighing bullshit all day and night.

Good job, Shaytoon. We are all very proud of you.
 
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