## I need a decorator!

Posted by Karl Sharman on April 1, 2014 – 6:06 am

Six house painters can paint six rooms in six hours. How many painters are needed to paint 100 rooms in 50 hours? There is the obvious solution, for which points will be awarded, but let’s put a little twist on this conundrum…. What if you can only fit one painter in a room at a time, or two, three, four five or finally 6 painters in a room at any one time?

April 1st, 2014 at 7:12 am

My guess is 12, but I don’t quite understand the extension. Maybe you mean that you can only have 1 room being painted at any time, but the question asks how many painters does it take, and here you’ve told us how many we can use. Maybe you’re asking how long it will take to paint 100 rooms with ‘x’ painters?

April 4th, 2014 at 11:49 pm

Sorry DP, to clarify… if you can only fit either 1,2,3,4,5 or 6 painters in the room that is being painted, how many painters will be required to complete the task of painting all 100 rooms in the 50 hours allotted. you can paint as many rooms as you like at the same time. hope this helps…

April 5th, 2014 at 2:48 am

From the initial premise 1 painter can paint 1 room in 6 hours, i.e each room takes 6 man hours. So 100 rooms would take 1 painter 600 hours, To do it in 50 hours would take 600/50 = 12 painters, as DP has stated.

With 100 rooms you can fit as many painters as you like into the one room (up to all 12) and it will still take 50 hours to complete the job.

Even with only one painter per room it is easy to schedule their activities so that there is no clash. For example, each painter can spend half an hour painting 1/12 of each room before moving on to the next one.

April 7th, 2014 at 6:56 am

If only one painter can fit in a room, then each painter takes 6 hours to finish a room. Thus, you need 13 painters to get the job done. Twelve painters can paint 96 rooms in 50 hours (well, really 48hrs, leaving not enough time for the remaining 4 rooms in two hours). An extra painter, working for 24 hours starting at hour 26 (or working at half speed starting at hour 2, or any other combo of rate and starting time that has him finishing at hour 50) is necessary to get the job done.

If only two people can fit in a room, then one room takes three hours to paint. Six teams of two painters (12 painters) can again paint 96 rooms in 48 hours. We need one extra painter to paint the four remaining rooms as per case 1 above, making 13 painters needed. But if weird physics or union regulations demand two people in a room, then we need an extra team of 2 painters, making 14 needed.

If you can fit 3 painters in a room, then each room takes two hours to paint. This divides evenly — 3 painters paint 25 rooms in 50 hours, meaning we need 12 painters to get the job done.

If you can fit 4 and only four painters in a room, then each room takes 1.5 hours to paint. In this case, 12 painters finish 99 rooms in 49.5 hours. Dang! We need one extra painter again, so 13 needed.

If five men can fit in a room, each room can be finished in 70 minutes. So five painters paint 41 rooms in 50 hours, ten painters paint 82 rooms in 50 hours, and the two spare painters paint 16 rooms in 48 hours. Meaning we have 98 rooms painted. Meaning we need that extra painter again to do the other two rooms. We need 13 painters. If we must fit five in a room then we need fifteen painters.

If we can fit six men in a room, then each room is painted in an hour. In fifty hours six painters paint 50 rooms, so 12 painters paint 100 rooms in 50 hours. Unless they work slow.