The Use of Knowledge Again
“Mathematics is the queen of sciences” (my older cousin, telling me the back of the head)

Many remember the old math problem: you have a hundred coins, one of them is fake and weighs slightly less than the others. For how many weights on simple scales, can you find this fake coin?
The algorithm of the solution is simple: on each cup of weights we put 50 coins. This is the first weighting.
The second weighing is the heap that is easier (due to the presence of a lighter counterfeit coin) again divided in half by 25 coins and weighed, comparing and finding the heap with a lighter coin.
The third weighing is 12 coins on each side. If the weight is equal, then the 25th remaining coin is fake.
The fourth is 6 coins.
The fifth is three coins.
The sixth weighing is to find a fake coin.

At the beginning of the 1990s, my friend and I made a large order for us: a survey of five different oncomarker employees of "Gorneftprodukt". This is a few oil bases and pieces of 50 gas stations throughout the area, people 800-900 approximately.
The technology is simple - a test tube with the blood of a particular person is divided into five probes and each drops the corresponding tumor marker-reagent. There is a reaction - the tumor marker worked, dragging this person for an in-depth examination and urgent treatment.
Reactants are expensive, “a single drop in a blood tube” cost, if I remember correctly, several hundred dollars.
The cost is high, the margin is low, take a lot.
We sit, we drop dumb, thousands of analyses still, batteries of probes in stalls, the entire laboratory is stuck... boring...
Someone has remembered this mathematical problem - and how does the desired blood differ from a fake coin?
Nothing is!! to
You take a cane, a drop of 100 people's blood in it, and I drop the reagent. No reaction - in the entire group of 100 people there is no lung oncology, for example. No need to check everyone.
If the marker worked - this group is divided into two, 50 people, and after a maximum of five iterations we find the patient.
In total, instead of 900*5=4500 studies, we fit in somewhere less than a hundred.
It was possible to take a drop of reactant for 900 drops of different people's blood at once, but we needed a guaranteed quality so that we couldn't miss anyone, and with such a different amount of blood we couldn't guarantee any unintelligible reaction.
Moreover, we repeated our scheme “for 100 people at a time” three times, for the same guarantee. And each time they changed the composition of the set of "100 drops of different people's blood".

The economic results:
-Instead of 4,500 studies, we settled with all possible reinsurance in 280 (this is a profitability of 1500% if I'm not mistaken)
The profit was enough to buy the "Soviet gentleman set": by apartment / machine / house.
“Everyone!” – “Operation Y”

The main results are medical:
- Identified 8 ACS operators and two drivers; seven - oncology of the first stage, one - the third, and two more - zero stage, something like "precancer" - the disease is not yet, but the marker is already working.
The third stage was late, and the person died.
“Thanks to our research, treatment started on time and the other nine people survived.