Once upon a time, in a kingdom beset by evil influences, a benevolent king condemed his court sorcerer to death for casting evil spells and being in league with the devil.
If you look at Figure 1, you will see stars. Stars come in various sizes: the figure shows the five-pointed star, or pentagram, which was the secret symbol of Pythagoras, the six-pointed star, or star of David, the seven-pointed star and the eight pointed star, or octopus.
What is a parabola? According to one small dictionary (brand-name suppressed), it is "the curve formed by the intersection of a cone with a plane parallel to its side."
Here, at last, are the results of the palindrome competition announced in Parabola, Volume 13, Number 3.
Thou shalt not covet, but tradition
Approves all forms of competition
In Volume 14, Number 2, under this title, we gave you some deliberately faulty "answers" to a number of standard problems.
Q.405 If $k$ and $N$ are positive integers with $k>1$, show that it is possible to find $N$ consecutive odd integers whose sum is $N^k$