DA. A Cake Conundrum

October 27, 2007 · answers, guests, math puzzles, numbers, The Mathcast · Permalink

«« · · · »»

Dennis Shasha, author of Puzzles for Programmers and Pros
joins us once again, posing a cake conundrum!

Standard Podcast [ 6:10 ] Play Now | Play in Popup | Download

1 Comment »

  1. jlundell said,

    October 29, 2007 at 4:45 pm

    Well, Jeremy gets more cake. The real question is how does he maximize it? If Marie takes the smaller portion of the first cake and chooses her portion of the second cake, Jeremy will cut the second cake in half. If she chooses the larger portion of the first cake, she’ll only get a crumb of the second cake.

    So Jeremy cuts the first cake in the ratio 3:1, and no matter which portion Marie picks, she’ll end up with 3/4 of a cake (neglecting crumbs).

    If Jeremy cuts a smaller piece than 1/4 from the first cake, Marie chooses the bigger portion and gets more than 3/4, so he’s not going to do that.

    If Jeremy cuts a bigger piece than 1/4 (up to 1/2), Marie will take the smaller (but >1/4) plus half of the second cake, so she’ll end up with >3/4.

    So: 1 1/4 cake for Jeremy–assuming Marie consents to the entire arrangement.

RSS feed for comments on this post · TrackBack URL

Leave a Comment

You must be logged in to post a comment.

The Math Factor Podcast Website


Quality Math Talk Since 2004, on the web and on KUAF 91.3 FM


A production of the University of Arkansas, Fayetteville, Ark USA

Download a great math factor poster to print and share!

Got an idea? Want to do a guest post? Tell us about it!

Heya! Do us a favor and link here from your site!