SOLUTION TO PROBLEM 14

Let's go backwards and take the last tip back. John had $ 2 before leving the 4-th restaurant and this was half of the sum he had in his pockets after entering this restaurant and tipping the doorman, so he had $ $2\times 2=4$. Adding to that the tip given at entrance one can easily see he had exactly $ 4+1=5, before entering the last of the 4 restaurants. Now let's go further backwards and "recuperate" the money spent according to the algorithm outlined above. One gets:

3-rd Restaurant:

$ $5+1=6\quad 2\times 6=12\quad 12+1=13$

2-nd Restaurant:

$ $13+1=14\quad 2\times 14=28\quad 28+1=29$

1-st Restaurant:

$ $29+1=30\quad 2\times 30=60\quad 60+1=61$

so initially he had exactly $ 61.

Questions and/or comments should be directed to Judy Downey or Griff Elder
 

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Last modified:   Wed Apr 18 16:26:41 CDT 2001