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# Math Circle Puzzle, Ball Throwing Number Game and I.C.E. Word Puzzle

The solutions to these puzzles can be found at the bottom of the page. Try to resist peeking until you have given yourself time to try to solve the puzzles.

## Slicing a Circle Math Puzzle

This was the first puzzle to show up in Sam Loyd's book "Cyclopedia of 5000 Puzzles Tricks and Conundrums with Answers". The puzzle simply asks, "How many pieces can be created by slicing a circle with seven straight lines". In Sam Loyd's version a German pancake was used.

## Sword Problem

A tricky scientific and practical problem from Sam's book. Why is the blade of a scimitar always shown to be curved?

## Right Triangle Math Puzzle

Sam Loyd enjoyed creating or enhancing classic math puzzles. Here is a question based on the Pythagorean theorem. If one side of a right triangle is 47 meters long, how many meters would it take to enclose the entire triangle?

## Throw a Fifty Math Puzzle

Here is a fun number game to try. The goal of the game is to throw the baseballs so that the number total comes to exactly 50. You can throw as many balls as you want as long as the total does not exceed 50. Simply click on a ball to throw it. If you go over 50 you can press the reset button and try again. Good luck.

## Words That End in I.C.E. Word Puzzle

Sam Loyd didn't just create math puzzles. He also enjoyed word puzzles. To complete the next puzzle, fill in the blanks in the following short tale using only words that end with the letters I.C.E. The list of the words in alphabetical order on the right will shrink as you find each word. After entering a word, press the TAB button to move to the next word.

# Solutions follow. No peeking!

### Slicing a Circle

The solution was not provided for this problem due to a contest that Sam Loyd was running when he wrote his book. We here at Softgame Company attempted to solve it on our own. We succeeded and got proof on some well-known mathematics sites. The circle slice problem can be solved by simply searching for a mathematical pattern as each line is cut. You can actually start the pattern with zero cuts. Here is a small chart showing the amount of pieces produced per cut.

• 0 cuts makes 1 piece
• 1 cut makes 2 pieces
• 2 cuts makes 4 pieces
• 3 cuts makes 7 pieces

Three cuts can also produce just six pieces such as how a pie is traditionally cut. However, in this puzzle we need to produce as many pieces as possible per cut. If you look closely you can see we have already established a pattern. The next chart shows the maximum number of pieces that can be produced based on an amount of cuts. The first number is the number of cuts. The second number is the amount of pieces from the previous cut. The final result contains the maximum amount of pieces produced.

• Zero cuts produces one piece.
• 1 + 1 = 2
• 2 + 2 = 4
• 3 + 4 = 7

If you add the amount of cuts to the previous cut's amount of pieces produced you can predict the amount of pieces for each additional cut. This way we can figure out mathematically the maximum amount of pieces that can be produced with seven cuts. Let's continue the pattern.

• 4 + 7 = 11
• 5 + 11 = 16
• 6 + 16 = 22
• 7 + 22 = 29

We are basically cutting each piece from the previous cut in half. The answer to our puzzle is 29 pieces.

### Sword Riddle

The answer to this riddle is actually quite simple. The scimitar is curved so that it can fit into its scabbard.

### Right Triangle Puzzle

To come up with a solution to this math puzzle, one would square the number, in this case 47, to come up with 2,209. Next, divide the number by two to come up with 1,104, which is the base. Finally, add one to that number to come up with the final side of 1,105.

### Throw a Fifty Number Puzzle

This puzzle looked like a real stumper at first glance, but after a short period of studying it, we were able to solve it rather quickly. We noticed all the numbers except two (the 19 and the 25) were multiples of three. The number 50 is not a multiple of three, so we realized that at least one of the two numbers that were not multiples of three had to be included in the answer. We figured we had found a good starting point. However, there was more. No matter which number we chose, the remaining amount needed was still not a multiple of three. It turns out we needed to use both of the numbers. After selecting the two numbers we came up with 44. Now we only needed a six to come up with 50. So, the final answer to the puzzle is to select the 25, the 19 and the 6.

### Words That End in I.C.E. Word Puzzle

Here is the full story with all the words ending in I.C.E. included.

At the time of the summer solstice, the ice delivery man, whom no one should accuse of avarice or artifice, put up a notice at an office in his edifice, put the effect that with malice toward none he would give good service to all, without choice or prejudice. Accordingly, he supplied the young boy with licorice, the lawyer with practice, the doctor with a poultice, the judge with justice, the builder with a cornice and a lattice, the gambler and his accomplice in their den of vice with dice, the bridal party with rice, the clergyman with a surplice, the cat with mice, the drinker with juice, the geologist with pumice, the woodman with a coppice, the sailor with a splice, the dentist with a dentifrice, the dressmaker with a bodice, and none with the price. But in spite of all his efforts to supply ice to suffice, some people objected so strongly to his caprice, that they applied to the police for advice regarding a device, by which they might either push him into a crevice or over a precipice!