January 9, 2017


ALL DRESSED

At the burger joint, 80 people bought a single burger in the last hour.  Among these people, 60 added mustard, 65 added pickles, 70 added onions, and 75 added ketchup to their burger.  What is the least number of burgers that had all four toppings?
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There are two methods...
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Answer: 30 burgers

Method 1:  Put ketchup on 75 burgers, leaving 5 burgers plain.  Now add onions to 70 burgers, filling the 5 plain burgers and 65 of the ketchup burgers.  This leaves 15 burgers missing one of the two ingredients so far.  Put pickles on all of those 15 burgers and on 50 of the two-topping burgers.  Now we have 30 burgers with fewer than three toppings.  Put mustard on those 30, and then mustard on 30 of the three-topping burgers, making a minimum of 30 burgers with four toppings.

Method 2:  The total number of toppings is 69+65+70+75=270.  Put three different toppings on each of the 80 burgers.  This leaves 270-(3x80)=30 toppings unused.  These 30 toppings will go on 30 burgers that don't have that topping, making 30 the minimum number of burgers with four toppings.

Whew.