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# Problem Of The Week

## Definition

The Problem Of The Week (POTW) is a contest designed to challenge your thinking abilities through interesting mathematical problems and puzzles. The contest is open to everyone: students of all majors, faculty, high school students and the general public.

## Format

A new problem will be posted to this page every Monday at 3pm. The solution to a problem will be posted on Monday at 3pm, exactly one week after the posting of the problem.

## Submission

Solutions can be submitted in one of two ways:

• By email to: potw@sandiego.edu in the form of a PDF file, a scanned document or a Word document.
• By dropping a hard copy at the Math/CS main office in Serra 133.

The day and time of submission are important in the scoring process (see scoring below). The deadline for submission is exactly one week after the posting of the problem.

## Scoring

The first 10 correct solutions will earn 10 points. The next 10 correct solutions will earn 7 points, and all subsequent correct solutions will earn 5 points. The n participants (n to be determined) with the highest scores at the end of the semester will be awarded a prize.

## Problem #5

Week of March 3, 2014: Horsing around.

A wealthy sheikh died and left a collection of fine Arabian horses to his 3 sons. His will states that the first son shall have 1/2 of the number of horses, the second son 1/3 and the third son 1/9, and that no horse shall be killed. When they found out that there were 17 horses in the collection, the execution of the will became impossible. A clever judge found the following solution: he added his own horse to the collection to make it 18. He gave 1/2 of the new collection (9 horses) to the first son. He gave 1/3 (6 horses) to the second son and 1/9 (2 horses) to the third son. In total, he gave out 17 horses and his horse was left. He took it back and declared the case closed. Explain why the judge’s solution seems to work when the direct distribution was impossible.

## Top Scorers

•  Name  Institution  Points
Jesus Tonatiuh Otay Ranch HS 30
Ed Alexander USD 15
Danielle Riethmiller USD 10
Faith Barchers USD 10
Zheng Dai USD 10