Friday, February 11, 2011

Brain Teaser #002

Ready for a hardcore work out of the mind? Then enjoy solving this riddle:

You are given 9 gold coins and a scale. One of the coins weighs either less or more than the other 8 coins. By using only the scale to measure the coins 3 times, can you figure out the odd coin? And for extra special bonus points can you figure out if the odd coin is heavier or lighter?

Things you can do:
-Weigh more than two coins simultaneously
-Weigh unequal amounts of coins (3 on one side 4 on the other)
-Label or "mark" the coins

Things you CAN'T do:
-Use your hands to measure
-Add coins gradually in a single weigh
-Subtract coins gradually in a single weigh

1 comment:

  1. 123456789

    weigh coins 1,2,3 and 4,5,6
    weigh coins 1,5,7 and 2,6,8
    weigh coins 3,4,8 and 1,6,9 on the other

    assuming each gold coin weighs 1 ounce.

    Scale one will be
    scale 2 will be 2.9-3
    and 3-3

    Scale 3 was even, so we know all the coins in that run were not the odd coin, which instantly eliminates 6. Which means it will be either coins 2,5 or 7.

    Knowing this we look back at tests 1 and 2. Test 1 shows us that Test 1, which included numbers 2 and 5, weighed 3-2.9, with the side containing coin 5 weighing slightly less and the side containing coin 5 weighed slightly more.

    In test 2 we see that when coins 5 and 7 are weighed together, they weigh slightly less then coin two coupled with 2 good coins. We can now deduct from this that coin 5 is the odd coin.

    Test 1 potentially bad coins 2 and 5 were weighed with two coins that were known to be good, we can now deduct that coin 7 is not the bad coin. With that we can look at test 2 and it is coin 2 and 5 once again each with 2 known good coins, this time we know that if coin 2 is heaview then coin 5, then coin 2 is the answer but since the side with coin 5 was lighter, as was with the first test, we know that it has the defect.

    I don't know if I did this right but I got the result I wanted. Hopefully I did but that was a mindbender, thanks!