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|number = 149 |
|number = 149 |
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|image = LS149.png |
|image = LS149.png |
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+ | |puzzle = |
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+ | ;US Version |
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The ares of sections I and III are equal, but what about the area of section II? Is it less than, greater than, or equal to the area of I? |
The ares of sections I and III are equal, but what about the area of section II? Is it less than, greater than, or equal to the area of I? |
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+ | ;UK Version |
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⚫ | |||
+ | The diameter of a circle is divided into three equal lengths and those lengths are used to make the marble-like design shown in the diagram. |
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+ | |||
+ | The areas of section I and III are equal, but what about the area of section II? Is it less than, greater than or equal to the area of I? Choose from A, B and C. |
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+ | |hint1 = |
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+ | ;US Version |
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* The biggest semicircles in the diagram. |
* The biggest semicircles in the diagram. |
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− | * The medium-sized semicircles, |
+ | * The medium-sized semicircles, with a length two-thirds the circle's diameter. |
* The smallest semicircles, with a length one-third the circle's diameter. |
* The smallest semicircles, with a length one-third the circle's diameter. |
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Use these different-sized semicircles to help you solve the puzzle. |
Use these different-sized semicircles to help you solve the puzzle. |
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+ | ;UK Version |
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⚫ | |||
+ | Bear in mind the following three sizes of semicircle:<br /> |
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+ | * The biggest semicircles in the diagram. |
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+ | * The medium-sized semicircles, with a length two-thirds of the circle's diameter. |
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+ | |||
+ | Use these different-sized semicircles to help you solve the puzzle. |
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+ | |hint2 = |
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+ | ;US Version |
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The diameter of the medium semicircle is twice that of the small semicircle, so its area will be four times as large. |
The diameter of the medium semicircle is twice that of the small semicircle, so its area will be four times as large. |
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The big semicircle has a diameter three times as big as the small one, so its area will be nine times as large. |
The big semicircle has a diameter three times as big as the small one, so its area will be nine times as large. |
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+ | ;UK Version |
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+ | For example, take the area of the smallest semicircle to be 1.<br /> |
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+ | The diameter of the medium semicircle is twice that of the small semicircle, so the area will be four times as large. The big semicircle has a diameter three times as big as the small one, so the area will be nine times as large. |
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+ | |||
+ | Use these ratios to help with your calculations. |
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+ | |hint3 = |
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+ | ;US Version |
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Big - Medium + Small = |
Big - Medium + Small = |
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This should help you figure out how to determine the area of section II. |
This should help you figure out how to determine the area of section II. |
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+ | ;UK Version |
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⚫ | |||
+ | To work out the area of either I or III, use the three semicircles as follows: |
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+ | |||
+ | Big - Medium + Small = |
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+ | |||
+ | Replacing these with the areas we found in Hint 2 gives us: |
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+ | |||
+ | 9 - 4 + 1 = 6 |
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+ | |||
+ | So, can you see how it is possible to work out the area of II? |
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+ | |hintS = |
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+ | ;US Version |
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The big semicircle has an area of nine. Since it's a semicircle, the area of the whole circle is twice that, or 18. From this, subtract the size of the areas of sections I and III, and you're left with the area of II. |
The big semicircle has an area of nine. Since it's a semicircle, the area of the whole circle is twice that, or 18. From this, subtract the size of the areas of sections I and III, and you're left with the area of II. |
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All right then. What is it? |
All right then. What is it? |
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+ | ;UK Version |
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+ | If you've got this far, the rest is easy. Here's one way to do it: |
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+ | |||
+ | The big semicircle has an area of 9. Multiplying that by two gives the area of the whole circle, 18. |
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+ | |||
+ | Take away the areas of I and III, that we worked out in Hint 3, and you're left with the area of II. |
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|incorrect = |
|incorrect = |
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;US Version |
;US Version |
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Try to think of a simple way of solving this. |
Try to think of a simple way of solving this. |
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− | |correct = |
+ | |correct = |
+ | ;US Version |
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+ | Precisely! |
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The areas of I and II are the same! The best way to think about it is to use the three sizes of semicircles as shown above. If the ratio of the diameters is 3:2:1, then the ratio of the areas is 9:4:1. |
The areas of I and II are the same! The best way to think about it is to use the three sizes of semicircles as shown above. If the ratio of the diameters is 3:2:1, then the ratio of the areas is 9:4:1. |
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Using the ratios as a guide, we can compare the ares of I, II, and III and conclude that they are, in fact, equal. |
Using the ratios as a guide, we can compare the ares of I, II, and III and conclude that they are, in fact, equal. |
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+ | ;UK Version |
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+ | Marble-ous! |
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+ | |||
+ | The areas of I and II are the same! The best way to think about it is to use the three sizes of semicircles as shown above. If the ratio of the diameters is 3:2:1, then the ratio of the areas is 9:4:1. |
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+ | |||
+ | Using the ratios as a guide we can compare the areas of I, II and III, and conclude that they are, in fact, equal. |
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<div style="text-align:center;">[[Image:LS149S.png]]</div> |
<div style="text-align:center;">[[Image:LS149S.png]]</div> |
Revision as of 00:37, 12 April 2019
← | 148 - Glass Boxes | 149 - Marble Thirds | 150 - Lily Pad Leapfrog | → |
Marble Thirds (Marble Swirl Circle in the UK version) is a puzzle in Professor Layton and the Last Specter.
Puzzle
- US Version
The diameter of the circle below is divided into three equal lengths, and those lengths are used to make the marble-like design that splits the circle into three different-colored sections.
The ares of sections I and III are equal, but what about the area of section II? Is it less than, greater than, or equal to the area of I?
- UK Version
The diameter of a circle is divided into three equal lengths and those lengths are used to make the marble-like design shown in the diagram.
The areas of section I and III are equal, but what about the area of section II? Is it less than, greater than or equal to the area of I? Choose from A, B and C.
Hints
Solution
Incorrect
- US Version
Too bad!
There's a simple way to solve this puzzle. See if you figure it out.
- UK Version
Too bad.
Try to think of a simple way of solving this.
Correct
- US Version
Precisely!
The areas of I and II are the same! The best way to think about it is to use the three sizes of semicircles as shown above. If the ratio of the diameters is 3:2:1, then the ratio of the areas is 9:4:1.
Using the ratios as a guide, we can compare the ares of I, II, and III and conclude that they are, in fact, equal.
- UK Version
Marble-ous!
The areas of I and II are the same! The best way to think about it is to use the three sizes of semicircles as shown above. If the ratio of the diameters is 3:2:1, then the ratio of the areas is 9:4:1.
Using the ratios as a guide we can compare the areas of I, II and III, and conclude that they are, in fact, equal.
Professor Layton and the Last Specter | Puzzles in||
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