November 8, 2001 Professor Adrienne G. Lavine sent the following electronic mail message:

Two things you said helped me. The first was the hint to use parentheses, which did start me thinking about the distributive law. But prior to yesterday I had only thought about this briefly, had quickly discarded the possibility of a non-tricky solution, and had moved on to thinking of advanced uses of parentheses such as in binomial coefficients. After failing there, I put it aside.

But yesterday when you said it used 3rd grade math, I went back to the drawing board and thought of 24 as 6x4. In fact, here was the whole line of reasoning:

6 x 4 | |

(5+1)x(5-1) | |

5x(1+1/5)x(5-1) | [i.e., 5(1+(1/5))(5-1)] |

5x(5-1+1-1/5) | [i.e., 5(5-1+1-(1/5)] |

5x(5-1/5) | [in other words, 5(5-(1/5))] |

Thanks for the diversion!

29 Jan 2002 Version | http://www.cs.ucla.edu/~klinger/solution.html |