During a competition, numismatist Aditi has been given Rs. 200 in Rs.1 denominations. The judge asks Aditi to allocate the Rs. 1 denominations into a number of pouches such that any amount required between Rs.1 & Rs. 200 can be given by giving out a certain number of pouches without opening them. Aditi thinks and asks the judge to give her 'x' number of pouches to keep the money, where 'x' is the minimum number of bags required to keep the total money. Can you guess the value of 'x'?

9514 1404 393

  8

Step-by-step explanation:

If the bags can either be given or not, each bag can assume one of two states. In order for there to be 200 possible combinations of items in one of two states, there must be at least log2(200) = 7.64 items. The minimum number of bags is x = 8.

The contents of the 8 bags will be Rs. 1, 2, 4, 8, 16, 32, 64, 73.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11