File:Balance puzzle SMIL.svg

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Summary

Description

Interactive SVG using SMIL of a balance puzzle with inequality by CMG Lee. The five colours represent integer weights, not necessarily distinct, from 0 to 9 inclusive. In the SVG file, click the buttons until the correct code is shown.

Solution

Let B, G, Y, R and P be the weights of the blue, green, yellow, red and purple blocks, respectively. In the rightmost balance, B = P.

Next hint…

Y + G = 2 B + P, thus Y + G = 3 B.

Next hint…

As Y < G and G ≤ 9 (all weights are single-digit), Y ≤ 8.

Next hint…

In the second inequality from the left, Y > 2 R, thus R ≤ 3. If R were 4 or more, 2 R ≥ 8 (we established that Y ≤ 8 and Y > 2 R).

Next hint…

As the left branch has B + G = Y + 2 R, we can add each side to the each side of Y + G = 3 B: (B + G) + (3 B) = (Y + 2 R) + (Y + G). Cancelling, 4 B = 2 Y + 2 R, thus 2 B = Y + R.

Next hint…

Y + R must be even so that 2 B is an integer. Thus, Y and R have the same sign.

Next hint…

Possible values of (R, Y) are (3, 7), (2, 6), (2, 8), (1, 3), (1, 5), (1, 7), (0, 2), (0, 4), (0, 6) and (0, 8).

Next hint…

As Y + G = 3 B, G = 3 B − Y.

Next hint…

Possible values of (R, Y, B, G) are (3, 7, 5, 8), (2, 6, 4, 6), (2, 8, 5, 7), (1, 3, 2, 3), (1, 5, 3, 4), (1, 7, 4, 5), (0, 2, 1, 1), (0, 4, 2, 2), (0, 6, 3, 3) and (0, 8, 4, 4).

Next hint…

The only one satisfying Y < G is (3, 7, 5, 8). We can confirm Y + G = 3 B.

Next hint…
Thus, B = 5, G = 8, Y = 7, R = 3 and P = 5. The code is 58735.

Source

Own work

Author

Cmglee

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Licensing

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share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.

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File history

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	Date/Time	Dimensions	User	Comment
current	11:22, 20 December 2021	512 × 288 (16 KB)	Cmglee	Hide tick and recentre // Editing SVG source code using c:User:Rillke/SVGedit.js
	01:27, 20 December 2021	512 × 288 (16 KB)	Cmglee	Hide combination in thumbnail and remove ceiling // Editing SVG source code using c:User:Rillke/SVGedit.js
	12:42, 30 November 2021	512 × 288 (16 KB)	Cmglee	Add interactivity and purple weight
	15:17, 29 November 2021	512 × 256 (18 KB)	Cmglee	{{Information \|Description=Interactive SVG using SMIL of a balance puzzle with inequality by CMG Lee. The four colours represent integer weights, not necessarily distinct, from 0 to 9 inclusive. \|Source={{own}} \|Date= \|Author= Cmglee \|Permission= \|other_versions={{source thumb\|Omescape_balance_puzzle_SMIL.svg}} }} Category:Balance puzzles

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Short title	balance puzzle SMIL
Image title	Interactive SVG using SMIL of a balance puzzle with inequality by CMG Lee. The five colours represent integer weights, not necessarily distinct, from 0 to 9 inclusive. In the SVG file, click the buttons until the correct code is shown.
Width	100%
Height	100%

File:Balance puzzle SMIL.svg

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Creative Commons Attribution-ShareAlike 4.0 International

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b12bbf3db7b48b4746e435687edff511fa6ca565

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16,394 byte

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288 pixel

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512 pixel

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