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Problems of the Week

Last Updated: 2/4/07 3:22 PM

3 Pointer

A Glutonian and Its Money

On the Planet Glutonia, three Glutonians (Xoptar, Yipton, and Zeenor) are counting their money in units of Goobles. This is the value of the coins in their base-4 system.

4 Goobles = 1 Gibble
4 Gibbles = 1 Krooble
4 Kroobles = 1 Kribble

Xoptar has 2 Kribbles, 2 Kroobles, 2 Goobles, and half as many Gibbles as Yipton.
Yipton has 1 Gooble, 6 Gibbles, 1 Kribble, and twice as many Kroobles as Xoptar.
Zeenor has as many Gibbles as Xoptar and Yipton combined, along with 8 Goobles, 1 Kribble, and more Kroobles than Xoptar, but less than Yipton.
What is the value in Goobles of each Glutonian's money?

 

2 Pointer

Luigi's Lasagna

Luigi made 3 large lasagnas for the weekend dinners. The 4 kids finished a lasagna each night, but different kids ate different amounts.

On Friday evening, Alex ate one third of the lasagna, Frank and Joe each ate one quarter, and Luigi ate the rest.

On Saturday evening, Frank and Luigi each ate one third and Alex and Joe shared the rest equally.

On Sunday evening, Alex, Frank, and Joe had portions the same size as Luigi's Friday night portion. Luigi ate the rest.

Who ate the most lasagna during the weekend? From most to least, what portion of a whole lasagna did each person eat? Answers must be in simplest form.