A Coin Puzzle: My Two Cents (Plus 97 More)

Our friends at Penny Dell Puzzles recently shared the following brain teaser on their social media:

Naturally, we accepted the challenge.

Now, before we get started with this one, we have to add one detail: which coins we’re allowed to use. It’s safe to assume that pennies, nickels, dimes, and quarters are available, but the question doesn’t say anything about half-dollar coins.

So we’re going to figure out the correct answer without half-dollar coins available, and then with half-dollar coins available.

Let’s begin.

[Image courtesy of How Stuff Works.]

The easiest way to get started is to figure out the smallest number of coins we need to make 99 cents, since that’s the highest number we need to be able to form. Once we have that info, we can work backwards and make sure all the other numbers are covered.

For 99 cents, you need 3 quarters, 2 dimes, and 4 pennies. That’s 25 + 25 + 25 + 10 + 10 + 1 + 1 + 1 + 1 = 99.

Right away, we know we’re close with these 9 coins.

You don’t need more than 3 quarters, for instance, because your possible totals are all below \$1.

Now, let’s make sure we can form the numbers 1 through 24 with our chosen coins. (If we can, we’re done, because once we’ve covered 1 through 24, we can simply add one quarter or two quarters to cover 25 through 99.)

Our four pennies cover us for 1 through 4. But wait, there’s 5. And we can’t make 5 cents change with 4 pennies or 2 dimes. In fact, we can’t make 5, 6, 7, 8, or 9 cents change without a nickel.

So let’s add a nickel to our current coin count. That makes 3 quarters, 2 dimes, 1 nickel, and 4 pennies. (Why just 1 nickel? Well, we don’t need two, because that’s covered by a single dime.)

Our four pennies cover 1 through 4. Our nickel and four pennies cover 5 through 9. Our dime, nickel, and four pennies cover 1 through 19. And our two dimes, one nickel, and four pennies cover 1 through 29. (But, again, we only need them to cover 1 through 24, because at that point, our quarters become useful.)

That’s all 99 possibilities — 1 through 99 — covered by just ten coins.

[Image courtesy of Wikipedia.]

Well, we can apply the same thinking to a coin count with a half-dollar. For 99 cents, you need 1 half-dollar, 1 quarter, 2 dimes, and 4 pennies. That’s 50 + 25 + 10 + 10 + 1 + 1 + 1 + 1 = 99.

Now, we make sure we can form the numbers 1 through 49 with our chosen coins. (Once we can, we can simply add the half-dollar to cover 50 through 99.)

Once again, we quickly discover we need that single nickel to fill in the gaps.

Our four pennies cover 1 through 4. Our nickel and four pennies cover 5 through 9. Our dime, nickel, and four pennies cover 1 through 19. Our two dimes, one nickel, and four pennies cover 1 through 29. And our one quarter, two dimes, one nickel, and four pennies cover 1 through 54. (But, again, we only need them to cover 1 through 49, because at that point, our half-dollar becomes useful.)

That’s all 99 possibilities — 1 through 99 — covered by just nine coins.

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PuzzleNation App Review: Hedgehog Gardens

Welcome to the another edition of PuzzleNation App Reviews! Today we continue our quest to explore the world of puzzly games and apps for your tablet or smartphone!

Our resident app player and puzzle fiend Sherri has another intriguing game for us today, so let’s get down to business and dive into her review of Hedgehog Gardens for iPad and iPhone!

Hedgehog Gardens is an iOS game that offers a cute twist on a simple counting game. But in this case, it isn’t so simple at all!

A pretty efficient hedgehog has taken up residence in the Back Garden. His goal, and yours, is to clear out all of the vegetables. To do this, you must number the tiles from 1 to 36, while following specific rules. In much higher puzzles, you must count even higher!

[Where would you place a 3 to continue the
hedgehog’s clockwise path around the garden?]

Each Back Garden puzzle is divided into four different sections, each of which is filled with a different vegetable. There are three rules to follow in order to clear the vegetables and number the tiles: you must move clockwise around the board, you must move in a straight line from section to section, and you can’t revisit a tile.

Now don’t panic about where to start because when you start a puzzle, some of the tiles have already been numbered. Your goal is to complete the puzzle by guessing the remaining numbers and having the hedgehog follow a path from 1 to 2 to 3 and so on.

Once you complete enough Back Garden puzzles, you open up the Orchard, which has its own set of rules. There are other sections you can open once you complete enough puzzles.

If you enjoy counting and Sudoku-type games, this is a great game to play. You get over 1,000 puzzles spread over several sections. However, all of the puzzles are not immediately available. The more you play, the more you open. The sheer volume of puzzles will keep a player busy.

Counting and Sudoku-type games aren’t really my thing, but I find myself playing a puzzle here and there because they are puzzling and almost soothing. They are a pleasant way to work the mind. And I have to admit, the rolling hedgehog is very cute.

Ratings for Hedgehog Gardens:

• Enjoyability: 3/5 — If you enjoy Sudoku-type numbering games, this one is for you. The sheer number of puzzles, over 1,000, should keep you occupied for a quite a while.
• How well puzzles are incorporated: 4/5 — The puzzles get progressively harder and bigger the later you go into each section. Since each puzzle has a unique solve, you really need to think and puzzle out how to complete each one, especially with the rule changes in other sections.
• Graphics: 2/5 — They’re pretty basic, just static pictures related to each particular section. For example, pictures of vegetables in the Back Garden. The rolling hedgehog is rather cute.
• Gameplay: 2/5 — It’s pretty much the same thing through all of the puzzles. There are different rules for each section, but you’re really just counting. There isn’t much variety.

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