HW7 - EECS 203 DISCRETE MATHEMATICS Homework 7 Due Thursday...

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EECS 203: DISCRETE MATHEMATICS Homework 7 Due Thursday, November 8 at 4pm Put your name and discussion section number (not the meeting time) on the first page of your homework. Submit your homework to (a) CTools, as a PDF file, or (b) the drop box marked “EECS 203” in room EECS 2420. If neither (a) nor (b) is possible please turn in your homework at one of the discussion sections. 1. (4 points) There are 15 gold coins, all of which are identical except for one counterfeit coin, which is either slightly heavier or slightly lighter than all the rest. You have at your disposal a balance scale and wish to identify the counterfeit coin and decide whether it is heavier or lighter. Prove, using the pigeonhole principle, that it is not lighter) in 3 weighings. 1 2. (4 points) You select n + 1 distinct numbers from the set { 1 , 2 , . . . , 3 n } . Prove, using the pigeonhole principle, that there must be two chosen numbers that differ by at most 2.
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