LS036 - How Many Ones?

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How Many Ones?
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Puzzle Number 036
Puzzle Name How Many Ones?
Picarats Given 40 Picarats
Type Input
Location Market Center
Previous Puzzle LS035 - Candy Counter
Next Puzzle LS037 - Seven Coins

This is the thirty sixth puzzle in Professor Layton and the Last Specter. To access this puzzle, you must talk to Tweeds. In order to solve this puzzle, you must figure out how many times the boy would write the numeral 1 while writing numbers 1 to 120. After solving this puzzle, you will receive the course Tweed's Trip for the Train mini-game.

Contents

[edit] Hints

Hint One
    Try writing the numbers down and counting the 1s.

    Be careful with numbers with more than one 1, such as 11.

Hint Two
    The single digits are easy.
    There's just one 1.

Hint Three
    Think about the double digits.

    There's one 1 in 12 and two 1s in 11. There's also one 1 in every number from 12 to 19, for a total of eight. There are eight more in 21, 31, 41, 51, 61, 71, 81, and 91.

Super Hint
    What about the triple digits?

    There's a single 1 in 100, and two 1s in both 101 and 110.

    111 has three 1s, and there are two 1s in every number from 112 to 119. Are there any numbers you haven't considered yet? Don't forget about the 1 in 120, either.


[edit] Messages

[edit] When Failed

Too bad!

Are there any 1s that you missed?

[edit] When Completed

Precisely!

The numeral 1 comes up 53 times.

You have to remember to count it twice in 11 and three times in 111. If you keep this in mind, the problem is simple.

[edit] Solution

The numeral 1 will appear 53 times.

[edit] Progress

1355 Picarats and 138 Hint Coins.



Last edited by Squiggle today at 22:11
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