Measuring Rice 2
You are given a regular balance, a 1 g weight and only 2 bags[can be used to contain rice]. You want to measure 1 kg of rice accurately from a pile using these. What is the least number of times you have to use the balance?
Note: You can put rice in the bags only. You can't put the measured rice anywhere else other than the bag.
*solving the 1st problem(Measuring Rice 1) is recommended.
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1 solution
[put 1st bag on one side of the scale and 2nd bag on other side]
measure 1g rice with 1g weight. ->(1) [don't focus on these numbers now]
measure 2g rice with 1g weight and 1g rice. ->(1)
measure 4g rice with 1g weight and 3g rice(now 2g and 1g are mixed, so can't separate them anymore). ->(1)
measure 8g rice with 1g weight and 7g rice. ->(1)
measure 16g rice with 1g weight and 15g rice. ->(1)
measure 31g using 31g rice(no weight). ->(0)
measure 63g rice with 1g weight and 62g rice. ->(1)
measure 125g using 125g rice. ->(0)
measure 250g using 250g rice. ->(0)
measure 500g using 500g rice. ->(0)
Add this 500g and 500g to get 1000g.
now for a more general approach:
[This problem has a similar approach as the last one so not going to elaborate much.] First turn 1000 to binary, 1111101000. It has 10 digits. Now if you look closely, every digit can be assigned to the 10 commands given above [left to right is 1 to 10 like, I did above]. Here every assigned '1' command measures rice including 1g weight and every '0' command excludes the 1g weight to measure rice. So if any amount N is to be measured, first turn it to binary then use it to determine in which step you should take 1g weight and in which step you shouldn't.