Question

What is the weight of 28 coins

Answer 1

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weigh 2 coins.

case1: if they are a different weight weigh a third coin and you will have the fake coin.

case 2: if they are the same weight that is the weight of a true coin.

there are 26 coins left. split the pile into 4 groups of 5 with a 6th coin.

knowing the weight of the true coin, as you weight the piles you will know how much they should weigh (multiple of the true weight of tue coin).

weigh the piles until you find a pile with a conflicting weight

it will have 5 or 6 coins.

split the pile into 1 2 2 or 2 2 2

find the pile that doesnt weigh right.

if it has 2 coins weigh one of the coins. if its the wrong weight its the bad coin. of its the right weight its the good coin.

takes 3 to 2+5+3+1 = 11 weighings

3 to 11 weighings. (11 being an unusually large number of times)

this is assuming its not a scale that weighs piles against eachother and weighs individual piles

Answer 2

Weight of 1coin=((5*4)+1)/4g = 21/4g

Weight of 28 coins=(21/4)*28 = 147g