[CV086] Squares and Circles

086 - Squares and Circles

Squares and Circles is a puzzle in Professor Layton and the Curious Village. The puzzle must be solved in order to progress the story.

Puzzle

Sylvain brought you this diagram to see if you can help him with it.

Several circles and squares are pictured in the diagram below. How many times larger is the area of the blue square when compared to that of the red square?

Hints

Click a Tab to reveal the Hint.

Do you see the circle that touches the sides of the big blue square?

A smaller square sits inside the circle and touches it. Since the square is smaller than the circle, you can rotate it within the circle.

If you rotate the middle square 45 degrees, its corners will touch the sides of the large blue square.

At the same time, notice that this rotation has made it so that the red square's corners now make contact with the middle square.

Having trouble visualizing the rotation? Try drawing it on your screen.

From the rotation described in the second hint, draw two perpendicular lines from the outer circle through the middle to divide the squares into four quadrants.

Do this and you'll see that the middle square's area is equal to half of the blue square's. Go and try if for yourself.

Solution

Incorrect

Nope!

You don't need to work any high-level math to figure out the answer.

If you've been trying to solve this one with cold hard math, you might want to try a more simple approach.

Correct

That's right!

If you rotate the middle square 45 degrees as shown in the picture above, the answer becomes apparent.

The middle square has half the area of the large blue square, and the little red square has half the area of the middle square. Therefore, the little red square is one- fourth the size of the blue square.

The blue square is four times the size of the red square.

v · d · ePuzzles in Professor Layton and the Curious Village

Normal	001 002 003 004 005 UK 006 007 008 009 010 UK JP 011 012 013 014 015 016 017 JP 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 JP 035 036 037 038 039 040 041 042 043 044 045 UK 046 UK 047 048 049 050 UK 051 052 053 054 055 056 057 058 059 060 061 062 UK 063 064 065 066 UK 067 UK 068 069 070 071 072 UK 073 074 075 076 UK 077 078 079 080 081 082 083 084 085 UK 086 087 088 UK 089 090 091 092 093 094 095 096 UK 097 098 099 100 101 102 103 104 105 106 107 108 109 110 111 UK 112 113 UK 114 115 116 117 118 119 120 121 122 123 124 UK 125 126 127 128 129 130 131 132 133 134 135

Weekly	See here for weekly puzzles

Puzzle Index: CV · DB · UF · LS · MM · AL · VS · LMJ