Unexpectedly Intriguing!
24 February 2023

Ready for a seemingly simple riddle? What is the maximum value of U.S. coins you can have without being able to make exact change for one dollar?

Before you answer, a word of warning! According to the experts at Puzzling, there's no clever formula you can use to directly solve this problem. Instead, you have to more-or-less slog your way through it in a brute force-like process of trial and error! [Warning: Puzzling also provides the solution in their discussion. Click through if and when you're ready for it, but you may want to hold off until you've finished here first!...]

Fortunately, we can help automate that process! We've built the following tool to help you work through any solution you might like to try. Just enter the number of coins for each type and our tool will tally up their total value and help guide you toward a valid solution! If you're reading this article on a site that republishes our RSS news feed, please click through to our site to access a working version of the tool.

Combination of Coins
Input Data Values
Number of Half-Dollars
Number of Quarters
Number of Dimes
Number of Nickels
Number of Pennies

Combined Value of Coins
Calculated Results Values
Total Value of Coins
The Bottom Line

If you need a hint for how to find the solution, read on! You are looking for the highest value of a combination of coins that, if you were to add just one more coin of any type into the mix, whether it be a penny, nickel, dime, quarter, or half-dollar, you would be able to produce exact change for a U.S. dollar bill. Whether that's possible with more or less than \$1.00 in coins is something you will discover!

In this tool, we've omitted the one-dollar coin as an option because, by definition, this coin alone is exact change for a dollar, so having one would automatically wreck your chances of discovering the solution. Plus, despite the U.S. Mint's claims of one dollar coins being in circulation, in practice, these coins are so incredibly unpopular with the American public, they might as well not be.

Good luck!

Image Source: U.S. Mint.

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