the blood test riddle (number theory) A microbiologist has been given a set of $100$ blood vials. Exact one of those $100$ vials is positive to a concrete disease X. The microbiologist desires to send only $7$ vials for analysis. He can mix as many samples as he wants into $1$ vial. Which and how many samples should contain every to-be-sent-for-analysis vial so the microbiologist can determine which of $100$ vials contains the contagious blood?
Caution: All $7$ vials are supposed to be sent at once! (So binary search is not an option.)
Tip: The binary representation of $100$ is
  $1\cdot64 + 1\cdot32 + 1\cdot4  
= 1\cdot2^6 + 1\cdot2^5 + 0\cdot2^4 + 0\cdot2^3 + 1\cdot2^2 + 0\cdot2^1 + 0\cdot2^0=\\  
= (1100100)_2$   
 A: Do you already know the answer to this question?  You really should indicate that if you do.
I presume the microbiologist determines the $7$-bit representation of the sample number, and sends all samples with the highest-order bit set into vial $1$, the second-highest-order bit into vial $2$, and so on, with those samples with the lowest-order bit set into vial $7$.  This presumes that each sample can be divided into at least $6$ parts that are sufficient for analysis.  (There are fewer than $2^7-1 = 127$ samples, so there are no samples that will be put into all $7$ vials.)
ETA: Let me elaborate on how to interpret the results.  Suppose that the results come back and vials $2$, $5$, and $6$ are positive for Disease X.  Then we write out the $7$-bit binary number with $1$ in the second, fifth, and sixth position: $0100110$.  That is equal to $2^5+2^2+2^1 = 32+4+2 = 38$, so the $38$th sample was the one positive for Disease X.
A: Number the samples 1-100.
Vial 1: All those with sample number of the form 1xxxxxx in binary
Vial 2: All those with sample number of the form x1xxxxx in binary
Vial 3: All those with sample number  of the form xx1xxxx in binary
etc.
Vial 7: All those with sample number of the form xxxxxx1 in binary
