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Each of the bottles mentioned in this question contains $50 \; \text{ml}$ of liquid. The liquid in any bottle can be $100 \%$ pure content $\text{(P)}$ or can have certain amount of impurity $\text{(I)}.$ Visually it is not possible to distinguish between $\text{P}$ and $\text{I}.$ There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is $10 \%$ or more.

For example, suppose bottle $1$ contains only $\text{P},$ and bottle $2$ contains $80 \% \; \text{P} $ and $20 \% \; \text{I}.$ If content from bottle $1$ is tested, it will be found out that it contains only $\text{P}.$ If content of bottle $2$ is tested, the test will reveal that it contains some amount of  $\text{I}.$ If $10 \; \text{ml}$ of content from bottle $1$ is mixed with  $20 \; \text{ml}$ content from bottle $2,$ the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has $\text{I}.$ However, if $10 \; \text{ml}$ of content from bottle $1$ is mixed with  $5 \; \text{ml}$ of content from bottle $2.$ the test will not detect any impurity in the resultant mixture.

There are four bottles. Each bottle is known to contain only $\text{P}$ or only $\text{I}$. They will be considered to be “collectively ready for despatch” if all of them contain only $\text{P}$. In minimum how many tests, is it possible to ascertain whether these four bottles are “collectively ready for despatch”?
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