From time to time we come across a riddle that is perplexing and challenging almost to the point of frustration! Just as we are ready to pull out our hair that elusive solution comes - and shouts of "I get it now!!!" are heard. The following riddles are variations of the same basic problem - it's a weighty one - but worth it. We suggest you read and try to solve the first one and continue with the others in order given as each variation is just a little more difficult - at least we thought so. And now, the first of "weighty problems":
1. BAGS AND BEADS
You are given 5 bags. There are 10 beads in each of the bags. In four of the bags, the beads each weigh 10 grams. In the remaining bag, each bead weighs only 9 grams. All the bags and beads look identical. You must find out which bag has the lighter beads. The problem is that all the bags look identical and all the beads look identical. You can use a scale, but it has to be a single-tray scale, not a two-tray balance scale. Also, you may use the scale only once. How can you find out which bag has the lighter beads?
2. GOLD COINS
Now you should be able to solve this variation, no problem: You have 10 bags of gold coins, 10 coins per bag, 10 grams coin, but one bag of coins weigh only 9 grams per coin (because of low quality). How do you find out which bag contains low quality gold coins? You may use a scale only one time. Thanks to Jason Vuong for this variation!
You have 9 marbles: 8 of them weigh 1 ounce each; 1 weighs 1.1 ounce. The 9 marbles are all uniform in size, appearance and shape. You have access to a balance scale containing 2 trays - you may use the balance 2 times. You must determine which of the 9 marbles is the heavier one using the balance only 2 times.
4. NINE GOLD COINS
This one is a little more
difficult because you are not told if the object is heavier or lighter.
You have 9 gold coins. All 9 coins look exactly the same but one coin is a fake and is either lighter or heavier than the other 8 coins. You have a scale - balance type with 2 trays - but can only load it twice. How do you find the fake gold coin?
5. CASE OF THE COUNTERFEIT
Now, if you have been able to solve the four problems above, this final weighty problem should be "no problem" for you to solve! This one is taken from a book: More Games for the Super Intelligent by James F. Fixx. We think it is the most difficult!
You have 12 identical-looking coins, one of which is counterfeit. The counterfeit coin is either heavier or lighter than the rest. The only scale you have to use is a simple balance. Using the scale only three times (Note: not loading, but using for balancing), find the counterfeit coin.
So that's it for weighty problems from Just Riddles and More...! There are lots of variations of this type of problem - we hope you have enjoyed our selection of them!