Obviously one problem is having absolutely no data to go on. However one of the advantages of a career in Consultancy is that one learns ways around what otherwise would be something of a stumbling block.
The key is to have a methodology which ensures there is documentary evidence that can be presented to the client prior to invoicing to demonstrate that work has been done to an assured quality level (we luckily don't have to say what that level is).
In this study we propose to use the following methodology:
Stage 1: identify the possible activities or behaviours that will lead to Tillerman requiring to take painkillers
Stage 2: identify for each possible activity a probability or alternatively the number of cases that will occur during his vacation
Stage 3: identify for each possible activity the number of painkillers required
Stage 4: numerical compute from the data collected (see, even without actual real data we have created some!) the total number of painkillers.
This methodology can be submitted to the client at the kick-off to get sign-off, and ensure they can say to their stakeholders they are operating an evidence driven decision making process (ha!). For the sake of argument the vacation is considered to start at arrival at the airport and end at return.
So lets start with Stage 1, identification of things that might require painkillers:
a) The terminal (either ends) is crowded and noisy
b) Tillerman drinks and flys (not a good idea, given dehydration effect of altitude)
c) A crying baby is in the seat next to Tillerman (either direction)
d) The road to the hotel is very bumpy and the driver speeds, so his head hits the roof
e) During his stay he bumps his head on the boom of the boat he is sailing
f) During his stay he falls asleep in the sun
g) During his stay he has a celebration involving too many drinks including rum
h) During his stay there is a steel drum band playing as he is trying to sleep
i) He is caught by Mrs T checking out the local ladies on the beach and his excuse involving research for the blog is not accepted
j) Alas there was something in the water/salad/fruit which didn't agree with his stomach
Ok, that's pretty comprehensive list, so on to stages 2 and 3. Here we use the model to develop (good word that, doesn't imply anything made up) the numbers, and fire up Excel, the consultants friend.
Of course there are some issues about concurrency i.e. probability of two events at once, but that is covered by the half a pill factor. There are also other activities that are likely to only happen once (activities f. and i. spring to mind).
Hence using a formalised, quality controlled methodology and a mathematical model we can derive the answer.
Properly this should of course be given in a PowerPoint presentation which sticks to that great recommendation of tell them what you're going to say, say it, then tell them what you've told them.
But as this is an unpaid study lets just jump to the answer: 18
Drum roll or address to send invoice to please.