On Friday I posted this puzzle….

John and Erica live together and between the two of them have three chores to perform. The chores are (i) vacuuming the floors, (ii) mowing the lawn and (iii) feeding the baby. Each of the chores takes thirty minutes, and they only have 1 vacuum cleaner, 1 mower and 1 bottle of milk. What is the shortest amount of time in which John and Erica can complete the chores?

If you have not tried to solve it, have a go now. For everyone else the answer is after the break.

Many people think the answer is 60 minutes but actually the answer is 45 minutes. John could, for example, do the vacuuming whilst Erica does half of the lawn (30 minutes). Then Erica would feed the baby whilst John finished the lawn (15 minutes). Did you solve it? Any other answers?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

1. Knut-Sverre says:

Easy. Couldn’t quite figure out why this was a puzzle at all.

Fairly obvious that three 30 minute tasks shared between 2 people can be split between them to take 45 minutes in total, assuming neither of them can multitask. With multitasking the shortest time is the time it takes to do the longest task, in this case 30 minutes. As far as I can see the question didn’t clearly exclude multitasking.

2. Raymond says:

I got the answer but thought with a ride on mower you could feed the baby while mowing 😛

1. Goliath says:

Now that would be very manly!

3. Anders says:

Not entirely sure where you get the (14 minutes) from, guessing that’s a typo, otherwise it was easy

4. Navneeth says:

I went with ‘one hour’ answer, but then had a nagging feeling that that wouldn’t be using the available resources most efficiently.

5. Harry Lime says:

6. M says:

Yes got that. But half the lawn takes 15 minutes, not 14.

My alternative answer was to give the baby the bottle in his hands. At a certain age babies can drink from the bottle without you helping him. Then it takes 30 minutes. But that is a lousy answer.

7. Jack says:

I assumed this was a lateral thinking question and thought that ‘John and Erica live together’ meant they were the only people in the house. From there I assumed the baby must therefore either be John or Erica, leaving only one person to capable of performing the chores which would mean they would take an hour and a half to perform. I guess I overthought it, actually I think I underthought it

1. Greg23 says:

I’m surprised this wasn’t the answer/trick to the puzzle.

8. a) John: vacuum: 15min. Erica does half the lawn: 15 minutes.
b) John, finishes vacuum: 15 minutes. Erica feeds baby: 15 minutes.
c) John finishes the lawn: 15 minutes. Erica finishes feeding baby: 15 minutes.

It could have easily been any activity that is cut in half though.

9. Yep, that’s the answer I got. Yay me.

10. Donalbain says:

I am still puzzled. If John does the vacuuming while Erica does half of the lawn, why doesn’t Erica just do the whole lawn? And if she only gets half the lawn finished, why does he manage to get the whole vaccuming done when they take the same amount of time?

1. Donalbain says:

Never mind! Got it while on the toilet!

2. Chris says:

I think Richard’s explanation was a little unclear.

John does the vacuuming (30 minutes), while Erica does half of the lawn (15 minutes) and then feeds the baby (30 minutes).

Once John is finished vacuuming, he moves on to finish mowing the lawn (15 minutes).

There’s an overlap, Erica starts feeding the baby while John’s still in the middle of vacuuming, and John moves to the lawn while Erica is still half-way through feeding the baby.

Alternatively you can half them each do half of each task, cycling every 15 minutes, as seePyou said above (that’s also the method I came up with).

11. Billly says:

This reminds me of a similar problem:
John is planning to cross the desert in his car. The trip is 10 000 km long. John has bought 4 brand new tyres plus a spare for the trip, but a tyre becomes unusable after 8000 km. How can John complete the trip?

1. Easy: stop every 2,000 km (would that be 2 Megametres?) and swap one of the tyres that hasn’t been changed yet with the current spare (e.g. [a] FL SP, [b] FR SP(FL), [c] RR SP(FR), [d] RL SP(RR)). That way, each of the five tyres gets 8,000 km of use. Needless to say, John had better have several hundred dollars in his bank account at the end of the trip in order to replace all five tyres, and probably order a sixth if he plans to do any driving before the trip back!

2. Let’s try that example again, without the angle brackets!
[a] Front Left swaps with Spare
[b] Front Right swaps with Spare (former Front Left)
[c] Rear Right swaps with Spare (former Front Right)
[d] Rear Left swaps with Spare (former Rear Right)

Each tyre therefore spends 8,000km on the road and 2,000km in the boot (trunk).

12. safc4ever says:

31 Minutes:

1 minute to set up the robotic vacuum cleaner then 30 minutes for the other two jobs (1 each).

13. If anyone’s still having trouble, I had to diagram it before I could work it out. The diagram looks like this:

vaccum 30m lawn 15m
John |——————| |———-|

lawn 15m baby 30m
Erica |———-| |——————|

1. Gus Snarp says:

Yeah, I had to draw this out the same way.

14. Eddie (@edzeteito) says:

Didn’t get it, and am now kicking myself for 45 mins.

15. Mat says:

My answer is 30 minutes, just because John can also feed the baby while mowing the lawn and then Erica could also feed while vaccuming. Have you not multitasked before? 🙂

1. Red says:

That’s my answer as well, seriously! Or am I missing something?

16. Lazy T says:

Easy, easier than mowing or vacuuming, easier still would be tell the servants to do the work

17. JimC says:

I got a bit confused and ended up with John vacuuming the baby, Erica mowing the floors and then both of them feeding the lawn.

18. Todio says:

I got 30 minutes as well. As any parent of a baby knows you MUST learn to multitask while doing chores or nothing will ever get done around the house! So John begins mowing while Erica vacuums and simultaneously feeds the baby. After 15 minutes they swap chores. Presto, done in 30 minutes then they put the tyke to bed and Erica spends the remaining 15 minutes sorting and folding that mountain of laundry while John juggles the utility payments to keep all three )water, electricity and gas) on in their house with only enough money for two of the three. How about a puzzle based on THAT Mr. Wiseman? LOL!! (parent of 4 here…)

1. Greg23 says:

As did I.

2. Weston says:

I also got 30 minutes for the same reason. I have bottle fed a baby numerous times while doing other chores including vacuuming.

3. Seraphim says:

Yep, parent of 6 here, multitasking is a necessity. 🙂 If you’re vacuum cleaner is too loud, the baby won’t cooperate, but let’s assume you’ve been there, done that, and got an appropriate vacuum cleaner. Or better yet, a Roomba.

19. Smylers says:

I like how one of the constraints is “they only have 1 bottle of milk” — as though multiple bottles of milk would somehow help with feeding just the one baby!

1. Anders says:

Multipathed redundant bottles with automatic failover? Hypermodern baby

20. Julia says:

I got 45 minutes.

My alternative answer is ‘longer’ as surely the half hour needed to feed the baby should be split over several feeding sessions.

21. Homero A. Gonzalez says:

Many people think the answer is 60 minutes but actually the answer is 45 minutes. John could, for example, do the vacuuming whilst Erica does half of the lawn (30 minutes). Then Erica would feed the baby whilst John finished the lawn (15 minutes). Did you solve it? Any other answers?

Who is taking care of the Baby, while John is vacuuming and Erica is doing half of the lawn? (Vacuuming and mowing the grass are noisy activities so that definitely would wake the baby up) if it was sleeping… So unless the description of the puzzle changes to indicate the baby is sound sleep and/or somebody (a nanny) is watching him/her while John and Erica are busy, the answer does not work for me… or does it?

1. Gus Snarp says:

This made me laugh, because it is so true of trying to get things done with two parents and a baby. Inevitably, one parent is “on baby” as we say at my house. But with vacuuming included as one of the chores, this problem is actually solved. Babies young enough to be drinking from a bottle actually sleep best accompanied by white noise. You can often lay the baby in the crib and start vacuuming and they’ll be asleep in seconds, much easier than other methods of putting them to bed. Or you can carry them or wear them in a baby carrier and they’ll fall asleep while you vacuum. They love the movement, and find the sound relaxing. Not trying to be pedantic, I loved your thought on this, just wanted to share that vacuuming can be a parent’s best friend!

2. Berber Anna says:

What’s wrong with putting the baby in a playpen for 30 minutes?

3. Gus Snarp says:

Nothing is wrong with putting the baby in a playpen for 30 minutes, if the baby wants to be in the playpen for thirty minutes. In my experience that’s longer than they’ll put up with. They’ll either fall asleep, or they’ll start crying and sobbing continuously. If you think it’s OK to let them cry for 30 minutes, be my guest, but it always seemed gratuitous to me.

4. Berber Anna says:

I don’t know, I don’t have kids myself, but when I’m visiting with friends who have a young son, they’ll put him in the playpen (in the room with us) and he happily plays or sleeps for a few hours before he wants attention again.

5. Gus Snarp says:

Mine never did that. Your friends are quite lucky. The only way we get a few uninterrupted hours is if they’re sleeping. Maybe we’re doing something wrong 😉

22. Bonnie says:

Curious how it seems very consistent in the comments to have Erica vacuum and John mow.

23. SherryH says:

Homero A. Gonzalez writes: (Vacuuming and mowing the grass are noisy activities so that definitely would wake the baby up) if it was sleeping…

Actually, both vacuuming and mowing are a constant, droning ‘white noise’, which many babies sleep through quite well. When my kids were babies, it was more common for them to wake up the moment the noise stopped. (Very depressing to have baby snooze while you rush around doing chores, then wake up and demand attention as soon as you’ve sat down to take a well-earned rest!)

Also, the baby wouldn’t necessarily have to be asleep. I wouldn’t find it unusual for one parent to vacuum for 15 minutes while baby played in a playpen or in an adjacent room behind a baby gate, and then to feed baby while the other parent finished vacuuming.

24. Gus Snarp says:

I did not find this easy. I still don’t. I had to diagram it and even now my brain still wants it to be 60 minutes. Obviously some people think and compartmentalize time differently than others. I’m actually hoping I can learn something from this puzzle that I can apply to my own time management. If I was actually in this situation, I would never have thought to stop one chore in the middle and move on to another to reduce the total time spent.

25. Realistically, it is one hour, not 45 minutes: Man mows the lawn, Woman vacuums the carpet; then Man has a nap leaving Woman to feed baby.

26. Anonymous says:

This was a basic engineering econiomics question. However, the lesson here is that had John and Erica used protection, they would have been done in 30 minutes and could have gone out to party.

27. Berber Anna says:

I did solve it as above, but I maintain that they’d be done in 30 minutes if Erica breastfed and used a sling.

28. Of course, no optimization answer is complete without a proof that it is truly the minimal amount of time necessary!

Let t1, t2, t3 be the times (in minutes) that John spends on the three tasks and let T be the total time he spends, i.e. T=t1+t2+t3. Let v1, v2, v3 be the times that Erica spends on the three tasks, and let V=v1+v2+v3.

Note that by definition
v1=30-t1
v2=30-t2
v3=30-t3
We can rewrite this to:
v1=t2+t3-T
v2=t1+t3-T
v3=t1+t2-T
So
V=2(t1+t2+t3)-3(30-T)=90-T

The end time is equal to the maximum of T and V, so it is either T or 90-T. This means the minimal value for the end time is attained when T=90-T, i.e. when T=45. So yes, the answer is optimal :).

1. Some errors in the calculation. I mean, of course:
v1=t2+t3+30-T and so on for v2 and v3
V=2(t1+t2+t3)+3(30-T)