Homeopathy says water ‘remembers’ a substance after it’s diluted away. Just count. Each ‘C’ step dilutes 100-fold; by 12C you’ve diluted 10²⁴, and one mole of starting material (~6×10²³ molecules) is down to LESS THAN ONE molecule. A common 30C remedy has, on average, none of the original substance at all. Slide the dilution and watch the last molecule vanish. Verdict: DEBUNKED.
Each centesimal (C) step is a 1:100 dilution, so nC multiplies concentration by 10⁻²ⁿ. Starting from ~1 mole (6.022×10²³ molecules), the expected count after nC is 6.022×10²³·10⁻²ⁿ. That drops below 1 at n = 12 (the ‘Avogadro limit’); by the popular 30C, it is ~10⁻³⁷ — effectively zero molecules of the original substance in the whole bottle. There is no known physical mechanism by which pure water retains a structural ‘memory’ on any relevant timescale. A fail-loud self-check throws unless 12C leaves fewer than one molecule. ◆ VERDICT: DEBUNKED — you can count it yourself.
The molecule count is exact arithmetic (Avogadro + dilution). Whether a given remedy helps via placebo or regression to the mean is a separate question — this sphere only refutes the ‘the active ingredient is still in there’ claim, which the numbers close outright.