1023 coins

Question:

“Imagine you are given ten bowls and ‘1023’ one rupee coins

Now you are supposed to place all the 1 rupee coins in different bowls such that when somebody asks you for certain amount (ranging from 1 to 1023),you will have to return him ONLY BOWLS with coins summing up to exactly what he asked.”

(*Now its like if you place 100 coins in each of 9 bowls and 123 coins in the last bowl…and if he asks for 200..you can give him TWO BOWLS summing up to 200..but it should apply to all the numbers ranging from 1 to 1023….).

Answer Binary System solves it all….

Place 2*0(2 power 0),so 1 coin in FIRST BOWL.. ——sums up to 1—-

Place 2*1(2 power 1),so 2 coins in SECOND BOWL.—–sums up to 2—-

Place 2*2(2 power 2),so 4 coins in THIRD BOWL.——-sums up to 4—-

Place 2*3(2 power 3), 8 coins in FORTH BOWL.——sums up to 8—

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Place 2*8(2 power 8) 256 coins in NINTH BOWL—sums up to 256—

Place 2*9(2 power 9) 512 coins in TENTH BOWL—sums up to 512—

So,……………………………………………………………….total sums up to 1023

Now, you can give only bowls to any amount asked between 1 to 1023.

(For Eg. 821 is asked..10th bowl+9th bowl+6th bowl+5th bowl+3rd bowl+1st bowl— 512+256+32+16+4+1=821.)

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