Gold Bags
How many bags did you start?
There is a guard at every bridge. (4 Guards 4 bridges). John was allowed to take a # of bags of gold from the castle w / him. However, the guard at the first bridge demanded 1 / 2 bags of gold and 1 plus the bag. John met his request and proceeded to the next bridge. The guards at the bridge, second, third and fourth identical demands, which met John. When John finally crossed all the bridges, one bag of gold was left. How many bags began with John? Explanations would be helpful =)
The way to solve a problem like this is working backwards. John ended with a bag. How many bags do not need in the fourth bridge so we take half + 1 of their bags left him with 1? x – ½ x – 1 = 1 x – ½ x 2 = X / 2 = 2 x = 4 Therefore, reached the fourth bridge with four bags. Then in the third bridge, x – ½ x – 1 = 4 x / 2 = 5 x = 10 therefore had to have 10 bags of gold as he walked from the second bridge, the third bridge. He must have reached the second bridge with x – ½ x – 1 = 10 x = 22 22 bags of gold. And to have 22 bags gold during the journey between the first and second bridges, had to start with 46 bags of gold. Now let's see: started with 46 bags after the first bridge place, has 46 / 2 – 1 = 22 bags after the second bridge, is 22 / 2 – 1 = 10 bags after the third bridge, is 10 / 2 – 1 = 4 bags after fourth bridge, is 4 / 2 – 1 = 1 bag of gold. Grande, which is the right answer!
Jay Jay Pistolet – Bags of Gold
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