Napoleonic & ECW wargaming, with a load of old Hooptedoodle on this & that

Saturday, 25 April 2020

Hooptedoodle #361 - Home Physics Puzzle

This comes from a discussion I had with a friend on email - there is no trick to this, it is simply a bit of school physics, but I was surprised how much discussion it gave rise to. I thought I'd trot it out here - have a think about this...

A man who is working from home sets up an experiment with his children one afternoon, as part of their home-schooling. They like that kind of thing, apparently.

They place a boat in their (very small) swimming pool. The man climbs in, and takes on board a number of very large stones borrowed from the garden. When the ripples have stopped, his kids mark (very accurately) the water level on the side of the pool (not on the boat, on the pool side).

Once they have done this, the man very carefully drops all the stones over the side into the water. Again, when the ripples stop, the kids mark the water level on the pool side. We may assume that there is no loss of water through splashes, overflow, drainage, leakage or evaporation during the experiment, and that the kids can mark the level with unlimited precision.

OK then - when he dumps the stones overboard, does the water level in the pool

(1) rise

(2) fall

(3) stay the same

No prizes, obviously, just a bit of (supposed) fun. I won't publish any comments for a day or two, so as not to spoil the puzzle for anyone who cares - this will also allow me a couple of days before I have to reveal that there were no responses at all.



  1. I am guessing the level stays the same as the stones in boat already cause displacement. However as I understand it, when in the boat they displace by weight, but when in the water, they displace by volume, so I am sure my original answer is wrong :-)

  2. Sort of a twist on Archemeides and his "eureka!" moment when considering the matter of the purity of the gold composing the King's crown. I've forgotten the details of how Boyancy is handled, but when in the boat, the added rocks should cause the craft to displace additional water equal to the weight of the stones. When merely dropped overboard, the stones can only displace water equal to their volume... stones being generally denser than water (but not denser than Donald Trump), water displaced by their weight in the boat will be greater than that displaced by their volume.

  3. It'll stay the same; the stones (now in the water) counteracting any increased buoyancy of the boat, the amount of water being constant, if no evaporation has been allowed (a friendly god will be required or 100% humidity . . . eurgh!).


  4. I’m guessing the water level goes up since the large stones will now displace their volume of water?

  5. Surly its gotta fall, especially if the guys got a belly like mine?!?!

  6. hmm...OK so the boat displaces water, that's how it floats, based on its volume, 'cos it weighs less than the volume of water it displaces weighs? Err...maybe. So maybe that volume doesn't change when the stones are dumped in the water, but they will now themselves displace some more water, so the pool level will rise? Err... maybe.

  7. Stays the same - the boat would merely have sat lower in the water?

  8. Ahh Displacement and buoyancy, takes my back to my naval training classroom days nearly 50 years ago. .........
    Hated that stuff. (completely unconnected to my lack of aptitude I'm sure. )

  9. Rob sent a response by email:

    LOWER - An amusing one, as at first one is tempted to think nothing has changed but the stones on their own sink displacing a volume of water equal to their own volume whereas in the boat, assuming the boat doesn’t sink, they force the boat down to displace a volume of water equal in weight to the weight of stones which will be a greater volume of water. This assumes the stones are denser than water, i.e. not pumice or similar as you don’t actually say they will sink… ?

  10. I'll do a short follow-up post - thanks to everyone that had a go, and/or thought about it!