Aspire Faculty ID #16499 · Topic: NIMCET 2009 · Just now
NIMCET 2009

Divide Rs. 1074 (in whole Rs., having incremental amounts) into a number of bags so that any amount between Rs. 1 and Rs. 1074 can be given by selecting some bags without opening them. What is the minimum number of bags required?

Solution

This is a binary-weight problem.
Minimum bags needed = smallest n such that
1 + 2 + 4 + … + 2ⁿ ≥ 1074

2¹¹ − 1 = 2047 ≥ 1074
So minimum bags = 11

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