The original puzzleSome restaurants make clients pay according to their means. There is a dollar entrance fee, the meal costs half of the money you have, and there is a tip of a dollar before leaving. How much money did you start with if you have none left after visiting 4 restaurants ? The SolutionThis enigma is quite similar to that of the apples and, once again, we start at the end -     1. At the fourth restaurant you paid "\$1 entrance, 1/2 of your money, and \$1 tip"          and had no money left.               "1/2 of your money" was evidently \$1 to leave the \$1 tip                    so you had \$2 before paying the meal plus \$1 to get in,                         \$3 on arriving at the restaurant.     2. At the third restaurant you paid "\$1 entrance, 1/2 of your money, and \$1 tip"          and had \$3 left.               "1/2 of your money" was evidently \$4 to leave the \$1 tip                    so you had \$8 before paying the meal plus \$1 to get in,                         \$9 on arriving at the restaurant.     3. At the second restaurant you paid "\$1 entrance, 1/2 of your money, and \$1 tip"          and had \$9 left.               "1/2 of your money" was evidently \$10 to leave the \$1 tip                    so you had \$20 before paying the meal plus \$1 to get in,                         \$21 on arriving at the restaurant.     4. At the first restaurant you paid "\$1 entrance, 1/2 of your money, and \$1 tip"          and had \$21 left.               "1/2 of your money" was evidently \$22 to leave the \$1 tip                    so you had \$44 before paying the meal plus \$1 to get in,                         \$45 on arriving at the restaurant. MathematicsThe formula for the money required, in terms of the number of reataurants,     is not as simple as it was for the apples,          the \$1 entrance charge and the \$1 tip tripling the rate of increase.If "n" represents the number of restaurants,     the number of dollars at the very start will be 3(2n - 1).               Once again the usual 2n - 1 formula.          For 10 restaurants you would need \$3069, a tidy sum !