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While exploring a remote island under the project "Search for Knowledge Program", Archaeologist "LALO" has found a hidden stargate which will open a portal to the Knowledge Dimension.

In order to start the stargate, we have to enter the stargate key (password), which can be derived from the "Page of Shapes".

The "Page of Shapes" has a design which is formed by different shapes. Every shape is part of a circle, and they are numbered from 1 to 75.

We have to use the available shapes to form a maximal number of same-sized circles, and have to ensure a minimal number of shapes remain unused (which are not and cannot be part of any circle formation).

The password is the maximal count of equal size circles formed and the minimal count of remaining shapes (as explained in "Page of Hints").

Help LALO to find the correct password (number of equal size circles, and count of remaining shapes) and unlock the Knowledge Portal!

Warning:
After three wrong attempts, the stargate will be automatically destroyed, along with the island!

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    $\begingroup$ a? b? c? hah - bang goes the island $\endgroup$
    – JMP
    Commented Jan 9, 2017 at 7:24
  • $\begingroup$ @ JonMark Perry: sorry didn't get this a? b? c? $\endgroup$
    – Dharmesh
    Commented Jan 9, 2017 at 7:47
  • $\begingroup$ Warning: After three wrong attempt stargate will be automatically destroyed along with island $\endgroup$
    – JMP
    Commented Jan 9, 2017 at 7:48
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    $\begingroup$ @JonMark Perry Thanks for saving island:-) ...corrected :-) $\endgroup$
    – Dharmesh
    Commented Jan 9, 2017 at 7:55
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    $\begingroup$ Are rotations possible? I.e. are "6", "7", "8", and "9" different shapes? $\endgroup$
    – Dark Matter
    Commented Jan 9, 2017 at 13:06

2 Answers 2

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I tried my best to cut and paste design and arrange in maximum possible equal sized circle And here is the Ans to start the stargate by 12 circle combination with 2 remaining shape

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I see 10 circles and 13 left overs.

Methodology for pen and paper. Group them into shapes that are alike so you can see how many of them there are. So...

For example: 22, 34, 48, (66+11) become one set 4 shapes that you can use (picking (66+11) first.

Ergo.

Circle Number) Shapes in it
1) 1, 5, 72, 74
2) 6, 7, 8, 9, 22
3) 13, 14, 15, 16, 34
4) 26, 27, 28, 29, 48
5) 11, 39, 40, 41, 42, 66
6) 54, 55, 62, 63
7) 60, 61, 69, 70
8) 17, 19, 65, 67, 68
9) 18, 43, 47, 75
10) 46, 49, 50, 53
Left over: 2, 3, 4, 23, 24, 25, 44, 45, 51, 52, 64, 71, 73

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  • $\begingroup$ Matter very much on right direction Hint: If we find out blueprint(outlines slightly visible in light red color) of diagram, we will be able to get more idea to place remaining pieces of shapes $\endgroup$
    – Dharmesh
    Commented Jan 10, 2017 at 10:55
  • $\begingroup$ remaining shape count = 2 (one part of password) $\endgroup$
    – Dharmesh
    Commented Jan 13, 2017 at 10:29

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