Math Department

Problem of the Week

Deadline: Friday, Feb. 8

What is the problem of the week?
How do I submit a solution?

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Long Division?

 
 
When the eccentric recluse Count Von Divideski passed on, he only had three living descendents, his three grandchildren, Alice and Bob, who always did their homework, and the lazy good for nothing Carl, who lies and cheats, and generally doesn’t do his homework. The Count decided to give all his wealth, which was kept in safety deposit box in a Swiss bank, to Alice and Bob. He knew he could not trust Carl, so at the reading of the will Alice and Bob were each given secret numbers with the instructions to divide Alice’s number by Bob’s number in order to obtain the serial number for the Swiss deposit box. Carl was aware of the entire arrangement, but he did not have access to Alice and Bob’s secret numbers.

The next day, after Carl observed Alice and Bob heading out to the International Airport, he searched through the waste paper basket of Alice and Bob’s study room and found a scrap of paper with what was almost certainly the remnants of the long division that Alice and Bob preformed before leaving for the airport. Evidently they also did not trust Carl because they had made a great effort to erase all of their work. Displayed below is a reproduction of the work on the scrap paper, where each X represents the location of a heavily erased single digit. Will it be possible for Carl to reconstruct the actual long division and beat his siblings to the wealth? (Note that an X in one position might represent a 3 and an X in a different position might represent a 7, say.)

Can you reconstruct the long division?
 
 
 

Submit your solutions to Dr. Jeff Boyle, 1033 Cowley Hall, by 12 noon Friday, Feb. 8.   Include with your solution your name, major(s) and year in school if applicable.