Source: Mathematical Circus by Martin Gardner
Find a number base other than 10 in which 121 is a square number.
Making the most of your ice cream cone
You have a circular piece of paper with which to construct two hollow cones. You cut out a sector with an angle $\theta$ then glue together the straight edges of the sector. You can make the other one by stickgin together the straight edges of the residual paper.
Which angle $\theta$ should you choose in order to maximise the volumes of the two cones?
Polya Strikes Out
Source: Thinking Mathematically by John Mason, Leone Burton & Kaye Stacey
Write the numbers 1, 2, 3, … in a row. Strike out every third number beginning with the third. Write down the cumulative sums of what remains:
1, 2, 3, 4, 5, 6, 7, …
3, 4, 5, 6, 7, …
1, 2, 4, 5, 7, …
1=1; 1+2=3; 1+2+4=7; 1+2+4+5=12; 1+2+4+5+7=19; …
1, 3, 7, 12, 19, …
Now strike out every second number beginning with the second. Write down the cumulative sums of what remains. What is the final sequence? Why do you get this sequence?
More from Chalkdust
- 21 simple steps to draw your own Islamic pattern!
- Computational proofs, AI music and embarrassing surveys feature in our latest edition. Plus all your favourite puzzles & columns.
- Can you solve it?
- Letter writing, hospital visits, and getting the family active are among the topics of discussion in this issue's Dear Dirichlet advice column
- How do you like your numbers? Prime? Positive but infinitely small? Find out which famous mathematician you are
- Fashion is fleeting, Chalkdust regulars are not.