Tom bought $$1000$$ bottles of solution for his science laboratory. Among them, one bottle had poison in it. If mixed with chemical $$X$$, this poisonous solution changes colour, while the colour of the solutions in other bottles would be unchanged. For each bottle, every mixture with $$X$$ requires one test tube, and it takes $$6$$ hours for any colour change to be observed. What is the least number of test tubes required for Tom to be able to identify the bottle with poison in it after $$6$$ hours?~\uline{~~~~~~~~~~}~ 
Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems->Solving Problems by Solving System of 
Binary Linear Equations with Integer Coefficients 