Color Junction

I came across an interesting and addictive puzzle game recently called Color Junction. It was created by Mihai Parparita of Google and is based on SameGame (formerly Chain Shot!) by Kuniaki Moribe.

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Balancing Acts

You are given 8 billiards balls, numbered 1 to 8, identical in shape and size. All but one weigh exactly the same. The odd ball is either heavier or lighter than the others. Using just three weighings on an ordinary two-pan balance, find the odd ball out as well as whether it is heavier or lighter than the others.

If you solve the previous puzzle, solve the same problem for 12 billiards balls (instead of 8) while keeping the maximum weighings to just three. Yes, there is a solution for this puzzle - if you give up, you can find the solution here.

For the first puzzle (with just 8 billiards balls), here is my solution (obfuscated using rot-13):

1. Xrrc onyyf ahzorerq 1, 2 naq 3 ba bar cna naq 4, 5 naq 6 ba gur bgure.
2. Vs gurl onynapr, gurl ner nyy abezny naq bar bs 7 naq 8 vf gur bqq onyy. Jrvtu 7 ntnvafg 1.
3. Vs gurl onynapr, 8 vf gur bqq onyy naq lbh pna svaq vgf bqqvgl ol jrvtuvat vg ntnvafg 1.
4. Vs gurl qba'g onynapr, 7 vf gur bqq onyy naq lbh jvyy vzzrqvngryl xabj vs vg vf urnivre be yvtugre guna gur bguref.
5. Vs gur onyyf qba'g onynapr va fgrc #1, bar cna jvyy tb qbja. Jvgubhg ybff bs trarenyvgl, nffhzr guvf vf gur bar pbagnvavat 1, 2 naq 3. Rvgure bar bs 1, 2 naq 3 vf urnivre guna gur bguref be bar bs 4, 5 naq 6 vf yvtugre guna gur bguref.
6. Xrrc 1 naq 5 ba bar cna naq 4 naq 2 ba gur bgure. Xrrc 3 naq 6 nfvqr.
7. Vs gurl onynapr, bar bs 3 naq 6 vf gur bqq onyy. Sebz fgrc #5, jr pna pbapyhqr gung rvgure 3 vf urnivre guna gur bguref be 6 vf yvtugre guna gur bguref. Jrvtu 3 ntnvafg 1.
8. Vs gurl onynapr, 6 vf gur bqq onyy naq vf yvtugre guna gur bguref.
9. Vs gurl qba'g onynapr, 3 vf gur bqq onyy naq vf urnivre guna gur bguref.
10. Vs gur onyyf qba'g onynapr va fgrc #6, rvgure gur cna jvgu 1 naq 5 jvyy tb qbja be gur cna jvgu 4 naq 2 jvyy tb qbja.
11. Vs gur cna jvgu 1 naq 5 tbrf qbja, sebz fgrc #5 jr pna pbapyhqr guna rvgure 1 vf gur bqq bar bhg naq vf urnivre guna gur bguref be 4 vf gur bqq bar bhg naq vf yvtugre guna gur bguref.
12. Jrvtu 1 ntnvafg 8. Vs gurl onynapr, 4 vf gur bqq bar bhg naq vf yvtugre guna gur bguref. Vs gurl qba'g, 1 vf gur bqq bar bhg naq vf urnivre guna gur bguref.
13. Vs gur cna jvgu 4 naq 2 tbrf qbja va fgrc #10, sebz fgrc #5 jr pna pbapyhqr gung rvgure 2 vf gur bqq bar bhg naq vf urnivre guna gur bguref be 5 vf gur bqq bar bhg naq vf yvtugre guna gur bguref.
14. Jrvtu 2 ntnvafg 8. Vs gurl onynapr, 5 vf gur bqq bar bhg naq vf yvtugre guna gur bguref. Vs gurl qba'g, 2 vf gur bqq bar bhg naq vf urnivre guna gur bguref.
15. Va fgrc #5, vs 4, 5 naq 6 tb qbja, pneel bhg gur erznvavat fgrcf ol fjnccvat 1, 2 naq 3 jvgu 4, 5 naq 6 erfcrpgviryl.

I confess that I had to finally give up while trying to solve the 12-ball variation in the second puzzle.

Another River Crossing Puzzle

Most of us would have seen the standard river crossing puzzle. However, Prasadini recently sent me another river crossing puzzle (Flash animation) that I think is far more challenging.

A father and his two sons, a mother and her two daughters, a thief and a policeman are on one side of a river. There is a boat by the river bank, but it can only take two people at a time. Only the father, the mother and the policeman know how to operate the boat. The father can not be with any of the girls without their mother around. The mother can not be with any of the boys without their father around. The thief can not be with anyone else without the policeman around. How can you get everyone across to the other side of the river?

Start the game by clicking on the big round blue button. Click on a person to get him or her on or off the boat. Click on the levers to get the boat to move.

It took me a fair bit of time to crack it and here is my solution (obfuscated using rot-13):

1. Gur Guvrs naq gur Cbyvprzna pebff bire.
2. Gur Cbyvprzna pbzrf onpx (Gur Guvrs qbrf abg eha njnl jura yrsg nybar!).
3. Gur Cbyvprzna naq n obl pebff bire.
4. Gur Cbyvprzna naq gur Guvrs pbzr onpx.
5. Gur Sngure naq gur bgure obl pebff bire.
6. Gur Sngure pbzrf onpx.
7. Gur Sngure naq gur Zbgure pebff bire.
8. Gur Zbgure pbzrf onpx.
9. Gur Guvrs naq gur Cbyvprzna pebff bire.
10. Gur Sngure pbzrf onpx.
11. Gur Sngure naq gur Zbgure pebff bire.
12. Gur Zbgure pbzrf onpx.
13. Gur Zbgure naq n qnhtugre pebff bire.
14. Gur Guvrs naq gur Cbyvprzna pbzr onpx.
15. Gur Cbyvprzna naq gur bgure qnhtugre pebff bire.
16. Gur Cbyvprzna pbzrf onpx.
17. Gur Cbyvprzna naq gur Guvrs pebff bire.

See if you can come up with a better solution.

Google Quiz in FOSS.in 2005

With a little help from the Google search engine (the irony!), I have found the sources of "inspiration" for the questions asked in the "Google Quiz" (GQ) in the recently concluded FOSS.in 2005.

The first problem was the same as #2 in the problem set for the 9th World Puzzle Championship (Qualifying Test) (PDF). The second problem was the same as #2 in the 2002 US Championship Puzzles. The third problem was the same as #1 in the 2000 US Championship Puzzles. The fourth problem was essentially the same (verbatim, except for the actual numbers) as #22 in the problem set for the 10th World Puzzle Championship (Qualifying Test) (PDF).


Not being someone who solves puzzles regularly (except for Sudoku, of course), I was quite impressed by these problems since most of them involved considering multiple alternatives, proceeding with one of the alternatives and then backtracking and proceeding with another if that proved invalid, continuing till one finds a solution. They should also be fun to solve using computer programs. (I know of at least one person who did precisely that.) I had asked some of the people at the Google booth if I could reproduce these puzzles on my web site to share with my friends, but they were not sure of the copyright issues and clearance for publication. Well, now we know where they got the puzzles from and have found some more interesting puzzles to work on!


(Originally posted on Advogato.)