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1. Four coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same. Draw a decision tree that gives an algorithm that identifies in at most two weighings the bad coin (but not necessarily de- termines whether it is heavier or lighter than the others) using only a pan balance. 2. Show that at least two weighings are required to solve the problem of Exercise 1.

1. Four coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same. Draw a decision tree that gives an algorithm that identifies in at most two weighings the bad coin (but not necessarily de- termines whether it is heavier or lighter than the others) using only a pan balance. 2. Show that at least two weighings are required to solve the problem of Exercise 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Four coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same. Draw a decision tree that gives an algorithm that identifies in at most two weighings the bad coin (but not necessarily de- termines whether it is heavier or lighter than the others) using only a pan balance. 2. Show that at least two weighings are required to solve the problem of Exercise 1.
Transcribed Image Text:1. Four coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same. Draw a decision tree that gives an algorithm that identifies in at most two weighings the bad coin (but not necessarily de- termines whether it is heavier or lighter than the others) using only a pan balance. 2. Show that at least two weighings are required to solve the problem of Exercise 1.
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