Wants to distribute 127 one rupees coins into different piggy bank so that any integer some from one through 21 Rs.27 can be paid by just handling over few or all the piggy banks without breaking open the piggy bank with the maximum possible numbers of big bang required?

Question

Answer

Problem:

Distribute 127 one rupee coins into different piggy banks so that any integer sum from 1 through 21 Rs.27 can be paid by just handing over few or all the piggy banks without breaking open the piggy bank with the maximum possible numbers of piggy banks required.

Solution:

Understanding the Problem:

In this problem, we need to distribute 127 one rupee coins into different piggy banks. We need to ensure that any integer sum from 1 through 21 Rs.27 can be paid by just handing over few or all the piggy banks without breaking open the piggy bank with the maximum possible number of piggy banks required.

Approach:

To solve this problem, we can use the concept of binary representation. We can represent the numbers from 1 to 21 Rs.27 in binary form with 5 bits, as the maximum sum we can get is 21 Rs.27.

Distributing the Coins:

We can distribute the 127 coins into the piggy banks in the following way:

For the first piggy bank, we can keep all the coins with the first bit as 1 (i.e., 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 Rs.27).

For the second piggy bank, we can keep all the coins with the second bit as 1 (i.e., 2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 21 Rs.27).

For the third piggy bank, we can keep all the coins with the third bit as 1 (i.e., 4, 5, 6, 7, 12, 13, 14, 15, 20, 21 Rs.27).

For the fourth piggy bank, we can keep all the coins with the fourth bit as 1 (i.e., 8, 9, 10, 11, 12, 13, 14, 15, 20, 21 Rs.27).

For the fifth piggy bank, we can keep all the coins with the fifth bit as 1 (i.e., 16, 17, 18, 19, 20, 21 Rs.27).

Explanation:

With this distribution, we can pay any integer sum from 1 through 21 Rs.27 by just handing over few or all the piggy banks without breaking open the piggy bank with the maximum possible number of piggy banks required. We can do this by using the binary representation of the required sum and selecting the piggy banks that correspond to the 1 bits in the binary representation. For example:

To pay 7 Rs.27, we can select the first, second, and third piggy banks as 7

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