Lockdown Lessons: Optimization
Growing up most of us must have solved the following question which went something like this: What is the minimum no. of weighing in a balance machine to be done to find the heavy coin in a pack of 12 coins?
The answer to the question is either two or three. The solution is that we make two groups of five coins and one group of two coins. We weigh the two groups of five coins and if both are equal then we compare the remaining two with any coin from the previous group. In case if the two groups of five coins are unequal then we further divide the coins from the higher side of the scale and split them into two groups of two coins and a single coin. This way we can figure out the odd coin.
What if we employ the same technique to test COVID - 19 patients? We will be able to increase our testing by a minimum of five times with the same capacity.
Till date, India has a maximum testing capacity of 18,000 per day (India plans to increase the test capacity to 1,00,000 per day in coming days). We can increase the testing capacity to 90,000 per day without additional spending.
India has been and is still very choosy with the respect to whom to test for COVID - 19. We follow a very strict protocol as to whom we should test and in spite of testing individuals with high potential, the percentage of people testing positive fluctuates between 2 ~ 5%.
Example: Till April 7th we have conducted 1,14,015 tests out of which 4616 samples came out as positive which means that around 4% of the samples tested positive.
On April 7th we have conducted 12,584 tests out of which 285 samples came out as positive which means that around 2% of the samples tested positive.
So in this case, if we mix 5 different samples as 1 sample and then run the COVID test (rt - PCR test) then we can eliminate 5 five samples at once if the result comes out negative. This helps in saving wells (PCR machines have wells into which small test tubes are inserted ) and if it turns out positive then we can further split those samples into groups of 2 or we can proceed with the individual tests as well. In this way, we have successfully increased our capacities without additional costs. The downside of this could be longer test time incase a certain batch turns out to be positive. I am confident that we can take this risk as the number of samples turning positive is incredibly low.
Note: This technique has been followed since a century. It is was used in World War 1 to rapidly screen people. (I don't know which side but my guess would be the Germans)
It is also used in coding: Binary Search Technique (If it rings some bells to the coders)
It is also not like my own out of the box discovered technique but it is rather a lesson from the past. Germany and Israel is currently employing the above technique.
Lockdown could be boring and if you are having any unsolved mysteries then you tell them to me here https://bit.ly/PuzzlingMysteries and I'll try to solve them.