Logic Development Problems
Puzzle #1 You have a measurement scale where on both sides you can put some balls for weighing. You have a set of eight balls, Seven balls weigh the same and one is heavier. You can not tell the heavier ball by holding it and you can only use the scale twice. How do you determine the heavier ball? Also, apply same logic to find out following: –What if you have 9 balls? –What if you have 12 balls? –How many weighing will you require in these two cases?
SOLUTION Puzzle #1
If we give a number for each ball, said form 1 to 8. We put ball 1, 2, and 3 on the left and ball 4, 5 and 6 on the right and weight them. If they are balanced then we know ball 1 to 6 are OK. We just need to put ball 7 on one side and ball 8 on the other side and weight them.
SOLUTION Puzzle #1 Otherwise, one side will be lighter. We just assume the left side is lighter we can just put ball 1 on the left, ball 2 on the right, weight them one more time. If they are balanced then ball 3 is lighter. Otherwise if left side is lighter, ball 1 is lighter. If right side is lighter, ball 2 is lighter.
SOLUTION Puzzle #1 Otherwise, one side will be lighter. We just assume the left side is lighter we can just put ball 1 on the left, ball 2 on the right, weight them one more time. If they are balanced then ball 3 is lighter. Otherwise if left side is lighter, ball 1 is lighter. If right side is lighter, ball 2 is lighter.
SOLUTION Puzzle #1 What if you have 9 balls? Divide the 9 balls into 3 groups of 3. Compare the weight of two of those groups. The heavier group should then be obvious, it will either tip the scales, or, if the scales stay balanced, then it is the group you didn't include.
SOLUTION Puzzle #1 What if you have 9 balls? Now, choose 2 balls from this group and compare their weights, and using the same logic as before, the heavier ball will be obvious
SOLUTION Puzzle #1 What if you have 12 balls? First, weigh all 12 balls, 6 on each side of the scale (weighing #1). Whichever side is heavier, take those 6 balls and weigh 3 on each side (weighing #2). Again, whichever side is heavier, take those 3 balls, placing 1 to the side, and weighing the other 2, one on each side of the scale (weighing #3 ).
SOLUTION Puzzle #1 What if you have 12 balls? During this weighing, if one ball weighs heavier than the other, the answer is obvious, and so too, if they balance perfectly, then the ball you put to the side is the heavier ball!
Puzzle # 2 There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly? Which box did you open and how can you be sure to label all boxes correctly?
SOLUTION Puzzle #2 The box that must be opened is the one labeled "apples and oranges." By definition, whichever fruit is inside, is the only fruit type that that box contains. If we found an apple in that box that was labeled with both apples and oranges;
SOLUTION Puzzle #2 Then it must therefore only contain apples, then you conclude that the box that is labeled "oranges" cannot contain only oranges, as all boxes have been said to be mislabeled. Thus, the box labeled "oranges" must contain both apples and oranges, leaving the box labeled "apples" to contain only oranges.
Puzzle # ? ? ? ? ? ?? ? ? ? ? ? ? Question 1: What is the next two rows of numbers? Question 2: How was this reached?
SOLUTION Puzzle #3 The next two rows will be
SOLUTION Puzzle #3 Explanation The first row simply a 1. The second row says that there is one 1 in the first row. The third row says that there is two 1’s in the above row. The fourth row says that there is one 2 and one 1 in the above row and so on…..