Maxwell has 1023 $1 coins. He divides and puts them into ten bags so that he can give out any amount between $1 to $1000 by giving the appropriate bags without changing the number of coins in each bag.
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Answer:
A dealer has 1000 coins and 10 bags. He has to divide the coins over the ten bags so that he can make any number of coins simply by handing over a few bags. How must he divide his money into the ten bags?
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A dealer has 1000 coins and 10 bags. He has to divide the coins over the ten bags so that he can make any number of coins simply by handing over a few bags. How must he divide his money into the ten bags?
The most logical way to go about solving such problems is to divide the given number by 2 if the number is even or add 1 to the number and divide by 2. Subtract the quotient from the Original Number (and not the modified number, if the original number were odd) and for the outcomes, keep dividing by 2 (as per odd / even logic, as explained) and keep noting the quotients, until you come to 1. If done correctly, you will see that all the quotients will add up to the original number. These quotients give the answer to the question posed.
Let’s see as to what the solution is:
We have 1000 coins and this being even number, we simply divide this by 2 and get the 1st quotient,
Step-by-step explanation:
1st Quotient is 500 and 1000 – 500 = 500
2nd quotient is 250 and 500 - 250 = 250
3rd quotient is 125 and 250 - 125 = 125 and being odd we consider it 126
4th quotient is 63 and 125 - 63 = 62
5th quotient is 31 and 62 - 31 = 31 and being odd we consider it 32
6th quotient is 16 and 31 - 16 = 15 and being odd we consider it 16
7th quotient is 8 and 15 - 8 = 7 and being odd we consider it 8
8th quotient is 4 and 7 - 4 = 3 and being odd we consider it 4
9th quotient is 2 and 3 - 2 = 1 and being odd we consider it 2
10th quotient is 1 and 1 - 1 = 0 and we come to the end of the solution.
Thus, here goes the way to divide 1000 coins into 10 Bags containing
500, 250, 125, 63, 31, 16, 8, 4, 2 and 1 coins.
500+250+125+63+31+16+8+4+2+1 = 1000.
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Answer:
102 dollars is the answer.