Cubes

Logic Level 2

A hiker walks into a cave, and finds an old man, who has 9 identical looking cubes. The old man gives him a set of weighing scales and says; "8 cubes are made of copper, and 1 is made of gold. The gold cube is marginally heavier than the copper cubes. If you can tell me which is the gold cube, you may have it."

Find the minimum number of weighing(s) needed for the man guarantee he walks away with the gold cube.

Image Credit: Flickr Jared Tarbell .

2 4 3 1

1 solution

Ryan Lumsden
Jun 18, 2015

The man chooses to weigh 6 cubes the first time, 3 on each side.

If the sides balance, he weighs 2 of the remaining 3.
If they balance, he knows the final cube is gold.

If the first weighing does not balance, he chooses to weigh 2 cubes of the heavier side.
If they balance, the third cube is gold,
and if they do not, the heavier cube is gold.

Moderator note:

Nicely done. What would the answer be if I'm given 10 identical looking cubes instead of 9?

Should be made clear it's a balance scale. I was messing around thinking its a conventional scale and couldn't get it below 4

Robert Liu - 5 years, 5 months ago

Reply to Challenge Master Note: 3 times...

Pankaj Joshi - 5 years, 11 months ago

I was thinking ten cubes instead of nine

gh dgfhdgf - 2 years, 12 months ago

Can't the answer be 1? If the man takes 8 of them, four in each hand, and if they weigh same, then the other left will be gold! So answer should be 1.

Naveen Attri - 5 years, 11 months ago

please take note the question asked GUARANTEE, what if you weigh 4:4 and one side is heavier?

Hau You - 5 years, 11 months ago

Wouldn't it be. The same ? He weights 5 and 5. Gets 4 from the heavier side and weigh them 2 and 2. If they balance then the one he left out would be the one. Therefore the minimum amount of weightings would be 2. If they did not balance the 2nd time, a 3rd weigthing would be needed.

Mateus de Almeida - 5 years, 11 months ago

how does he weigh 5 and 5 when he got only 9 cubes? anyway your answer isnt correct also, question asked for minimum to[ guarantee] * , yours is just minimum without guarantee, if so then the minimum would be just 1, which is by luck you got the heavier one when weighing 1:1 on the first time, which is clearly not what the question asked.

Hau You - 5 years, 11 months ago

@Mateus de Almeida sir replied to @Pankaj Joshi sir on the question asked by Challenge Master ..so, it has to be 10!!!

Yoogottam Khandelwal - 5 years, 11 months ago

So, your solution says 'If they balance' , well my friend, if they dont then you have to make one more measurement to get the defected piece. So to make sure you pick the right piece in min ways, 3 measurements are required.

Pankaj Joshi - 5 years, 10 months ago

Cubes

Image Credit: Flickr Jared Tarbell .

1 solution

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