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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 Fall '07
 YaoyunShi
 Combinatorics, Mass, Dice, Coin, counterfeit coin

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