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Thanks to Patrick from Woodbridge School for his thoughts responding to this problem.

Look at the Hint page for more links to information.

Here's what he says : Cholera is a bacterial disease that often kills, usually by dehydration or lack of vital salts. It causes extreme diarrhoea and vomiting, and the water loss from the dehydration causes the blood to turn black and the skin blue.

The main supporting evidence for the decision is:
... found that nearly all the deaths had taken place within a short distance of the [Broad Street] pump. There were only ten deaths in houses situated... nearer to another street-pump. In five of these cases the families of the deceased persons informed me that they always sent to the pump in Broad Street... In... other cases, the deceased were children who went to school near the pump in Broad Street...

... [There] were 61 instances in which... the deceased persons used to drink the pump water from Broad Street...

The result of the inquiry, then, is, that there has been no particular outbreak or prevalence of cholera in this part of London except among the persons who were in the habit of drinking the water of the above-mentioned pump well. This is strong evidence, but the evidence cannot confirm with absolute certainty that this is the cause - there could have been another cause unrelated to the pump, in which case the decision would have been incorrect.

Thanks Patrick