# color coded puzzle

Help me solve this problem. As this site appreciates a little effort from the person who posted it. Here's my thought process:

1) The matrix starts with 0 ( gr, gr, gr). It has three places which can take two different colors green and red so within the range(0-10) there are 2*2*2 = 8 possibilities. But numbers possible (0-10) = 11. Therefore some numbers have the same color coding. But that leads to confusion.

2) 0 ( gr,gr,gr)and 3 ( gr ,red,gr) meaning if I jump 3 numbers there's a new color which comes in the mid position This agrees with 21 ( bl,red,gr) 23(bl,bl,gr) and another thing is clear that the new color is placed over the previous color. Meaning the blue that is introduced in the last tile of 23 ( bl,red,bl) simply sits above the green tile of 21 and it simply jumps one step left in 24(bl,bl,gr) revealing the gr that lies under it. But that leads to confusion what would be 22?

• it seems like that this puzzle comes from elsewhere. please provide the source. unattributed work may get downvoted or even closed. happy puzzling ;) Jun 17, 2019 at 12:56
• I am sorry it's from a previous year exam paper which I am appearing. They always ask one question of this type. Are you suggesting I should also upload the main question paper as a reference? Jun 17, 2019 at 14:53
• The URL of where the exam comes from is ideal. If it’s not online, the title and year of the exam and whose exam it is. Basically, enough to adequately disclose and attribute the original source.
– Rubio
Jun 17, 2019 at 16:27
• Next time you can just edit that information into your question post. I’ve done that for you now.
– Rubio
Jun 19, 2019 at 12:49

This is a depiction of numbers in ternary (base 3). Effectively your right hand column represents 'ones', the middle column 'threes', and the left hand one 'nines' (in the same way that in decimal we have 1s, then 10s, 100s, etc.).

A green square implies a value of 0 in that position, red a 1 and blue a 2. e.g. 10 red-green-red = 101 in ternary, i.e. one 9 plus one 1, which equals 10 in the usual decimal system. Similarly our decimal 24 is 220 in ternary: two 9s plus two 3s, which is blue-blue-green, as above.

Your final calculation is: 100 x 002, which in decimal is 9 x 2, giving an answer of 18. This translates above as 200 in ternary, or blue-green-green.

• Can you tell me where I can find this kind more questions to solve? This was a sample question from an exam I will appear. They always ask this kind of question. Jun 17, 2019 at 14:56
• @RitwikBhattacharyya I would simply recommend looking up more past papers. The institution where you study may be able to assist - try asking a tutor. Some universities and colleges often keep an archive of past papers on their intranet site or a student portal. Some exam boards may also provide sample past papers on their websites. Alternatively, just search for different base systems online and get a feel for how they operate - they're all inter-related; you'll soon get used to the patterns involved. Good luck!
– Stiv
Jun 18, 2019 at 8:25
• PS Don't forget to mark this as the answer if it solved your problem! Thanks :)
– Stiv
Jun 18, 2019 at 8:25