## Difficult Danny

Math brain teasers require computations to solve.Difficult Danny has acquired his nickname (and some other, less polite nicknames) due to the fact that, whenever he buys anything, he insists upon paying the exact amount, with precisely 100 pieces of currency. Danny walks into McArnold's and orders an iced coffee for $1.99. He pours 100 coins onto the counter, using some number (possibly zero) of each of the following: pennies, nickels, dimes, quarters. There are equal, non-zero quantities of dimes and quarters. What is the breakdown of coins that Difficult Danny used to pay for his iced coffee?

(See hint for currency values.)

(See hint for currency values.)

## Comments

Posted by extremeblueness on Oct 21, 2013 How would he pay for anything that's 10,000,000.01+ US dollars? |

Posted by eighsse on Oct 21, 2013 Well, I can't say I know all about Danny's life, but I'm guessing that he is not lucky enough to ever encounter that problem. Perhaps he would use a check as one of the "pieces of currency." |

Posted by JimShorts on Oct 23, 2013 The opening line alone makes this teaser totally worth it! And brilliant response to the comment above, by the way! |

Posted by charlottes-odd on Dec 05, 2013 Eighsse could you pm me and tell me the method of how you figure this sort of problem out? (sorry for my stupid brain :laugh |

Posted by dewtell on Jan 03, 2015 You can solve this with algebra, but here's how I worked it out in my head in a few seconds: first, assume that he paid all in pennies. That would be 199 pennies. Now we know that he had at least one (quarter + dime) pair in his answer - so for each such pair, he would add two coins and take away 35 pennies, for a net reduction of 33 coins. Given that we start with 199 coins, it's obvious that if we do this 3 times, we wind up with 100 coins. |

Posted by eighsse on Jan 03, 2015 Very nice, dewtell. Of course, if there had been more than 0 nickels involved, you'd have had to dig a little deeper, but since there were 0, that method makes it a cinch. Good work! |

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