Here is a nice problem tweeted by the Republic of Mathematics:
Average of 3 consecutive cubes, n^3, (n+1)^3, (n+2)^3 is an integer. Same true if 3 replaced by odd integer?
— Republic of Math (@republicofmath) August 4, 2015
Free of the constraints of Twitter’s 140 character limit, let’s explain this problem in a little more detail. Continue reading
The solution to the Gridlock puzzle is now available:
The next puzzle will be the really hard one that I have been promising for ages. The Mad Hatter is back, and this time he’s wearing a stetson…
What would be your estimate of the combined volume of these boxes, in cubic metres, to the nearest 0.1? There are nineteen in total (including the flat one that you can see perched on top), of various sizes, pushed together fairly closely, though not tightly. The chair is included in the photo to give an idea of the scale.
A quick puzzle to keep things ticking over until the imminent return of the Mad Hatter. Suitable for A-level students and top-end GCSE, or even KS3. Has been known to stump maths teachers too:
#7: Gridlock
A deceptively simple puzzle. Fill in the grid.
Published: 29/07/2015
Difficulty: *
Maths knowledge required: Very basic – calculating means.
The solution will be available next week.
IMAGE: IDS.photos – Creative Commons
The giant crab that I have chosen to illustrate this post is not relevant to the puzzle, but bonus points go to anyone who knows why I have picked it and can provide an appropriate response… Continue reading
Stephen Morris has provided a very detailed response to this question, which I have copied to the end of the original post.
It turns out that my intuition was correct (the tiling is possible if and only if r is a rational number lying in the half open interval (0,1]), but the proof is not obvious. The maths involved seems to be rather lovely though, so Stephen’s comments are well worth a look.
For a mini-puzzle, scroll down to the bottom of this post…
A NEW SEQUENCE FOR THE OEIS!
Inspired by all that 82000 business (see HERE, HERE and HERE), I recently created another sequence centred on the idea of expressing numbers in different bases. Continue reading
Obviously, the tiles must not overlap one another and must not overlap the boundary of the blue square.
[UPDATE: See the bottom of this post for the answer to this question, provided by Stephen Morris.]
Following my piece on tennis and probability, here is another tennis article. There is not really much maths in this one, just carefully researched irrelevance (though there may be a more mathsy follow-up at some point). Oh, and I am not really claiming that any of these players are the worst. See the disclaimer!
Continue reading
The 82000 sequence is still generating interest.
Here’s a great Numberphile video about the sequence from mathematician James Grime:
[youtube http://www.youtube.com/watch?v=LNS1fabDkeA]
The sequence has also made it into the Online Encyclopaedia of Integer Sequences, as A258107!
I have also found an early mention of the special properties of 82000, in this exchange on a French puzzle forum, from October 2008. Continue reading
