Puzzle 5: A cow, a horse and a goat

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Solution to Puzzle 4:

 The solution to puzzle 4 was much more complicated than I imagined. My google gave many solutions. I liked this solution from Nytimes better. I am copying and pasting from nytimes

          Number the coins 1 through 12.

  1. First weighing: 1,2,3,4 v 5,6,7,8.
    1. If equal, weigh 9,10,11 v 1,2,3 (not counterfeit).
      1. If equal, 12 is the counterfeit and weigh it against any other coin to determine if it’s heavy or light. 
      2. If not equal, the direction of 9,10,11 will determine heavy or light. 
      3. The third weighing is 9v10. 
        1. If equal, 11 is counterfeit. 
        2. If not, which ever of 9 or 10 went the same direction as in the second weighing is counterfeit (and you’ll know heavy or light from the second weighing).


  1. If 1,2,3,4 v 5,6,7,8 is not equal, mark which way each side moved. 
    1. Let’s assume 1,2,3,4 went down and 5,6,7,8 went up.
    2.  The second weighing is 1,2,5 v 3,4,6 where three of the coins change sides. 
      1. If equal either 7 or 8 is counterfeit so weigh them against each other and which even one goes up is the counterfeit and it is light. 
      2. If 1,2,5 v 3,4,6 is not equal then three of the coins changed direction (since they’re on different sides of the balance scale for this weighing). 
        1. Those three are obviously not counterfeit since the counterfeit will always cause the scale to move the same way. 
          1. Let’s assume that 1,2,5 went down again. That means that either 1 or 2 is counterfeit and it is heavy. 
            1. Weigh 1 v 2 and which ever one goes down again is the counterfeit coin.

 

  1. On the second weighing of 1,2,5 v 3,4,6, if 1,2,5 goes down again, then either 1 or 2 is the counterfeit and it is heavy OR 6 is the counterfeit and it is light. 
  2. So, if on the third weighing 1v2 is equal, then 6 is the counterfeit and it is light. 

This is now the complete answer to the 12 coin problem.  

I tried to draw a very rough image for this logic. You should do too.


 

Puzzle 5: A cow, a horse and a goat

A cow, a horse and a goat mistakenly enter a farmer's wheat field and eat some stalks of wheat. The horse eats twice as many stalks as the goat, and the cow eats twice as many stalks as the horse. The farmer demands 5 kgs of wheat from the owners of the animals to replace what was eaten. How much wheat should be replaced by the goat's owner? by the horse's owner? by the cow's owner?

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