Problem #1
You are a cook in a remote area with no clocks or other way of keeping time other than a four minute sandglass timer and a seven minute sandglass timer. (The kind you turn over - hourglass shaped) You do have a stove, however, with water in a pot already boiling. Somebody asks you for a nine-minute egg, and you know this person is a perfectionist and will be able to tell if you undercook or overcook the eggs by even a few seconds. What is the least amount of time it will take to prepare the egg? And how will you prepare it so that it is neither undercooked or overcooked?
You are traveling down a path and come to a fork in the road. A sign lays fallen at the path indicating that one path leads to a village where everyone tells the truth and the other to a village where everyone tells lies. The sign has been knocked down so you do not know which path leads to which village. Then someone from one of the villages (you don't know which one) comes down the path from which you came. You may ask him one question to determine which path goes to which village. What question do you ask?
Person x and y have the following conversation:
x: I forgot how old your three kids are.
y: The product of their ages is 36.
x: I still don't know their ages.
y: The sum of their ages is the same as your house number.
x: I still don't know their ages.
y: The oldest one has red hair.
x: Now I know their ages!
How old are they?
How many addition signs should be put between digits of the number 987654321, and where should we put them, to get a total of 99?
Divide the face of the clock into three parts with two lines so that the sum of the numbers in the three parts are equal.
A man has to be at work by 9:00 a.m. and it takes him 15 minutes to get dressed, 20 minutes to eat and 35 minutes to walk to work. What time should he get up?
If you begin with a one digit number, multiply by 3, add 8, divide by 2 and subtract 6, you will get the number back.
Find the number.
Jane is older than Kim.
Kim is older than Shawn.
Shawn is younger than Jane.
Rachel is older than Jane.
List the people from oldest to youngest.
There are 12 people in a room. 6 people are wearing socks and 4 people are wearing shoes, 3 people are wearing both. How many people are in bare feet?
Kim, Raelene, Jim and Rick finished first, second, third and fourth in a motor bike race. If their numbers were 5, 17, 1 and 7, use the following clues to find out who had what number and in what order they finished.
- 17 said she would have placed higher if her bike had not stalled at the start.
- Rick finished before 7 but after Raelene.
- 1's father, said he was very proud of his daughter's finish.
- Kim finished after 5.
- Jim wasn't third.
Solution: The answer is 9 minutes. First, flip both hourglasses over and drop the egg into the water. When the four minute timer runs out, flip it again. When the seven minute timer runs out, flip it over. The egg has been cooking seven minutes. Now when the four minute timer runs out again (after eight minutes) flip the seven minute timer back over. Since the seven minute timer has been running only a minute between flips, there's a minute worth of sand left. And when that minute runs out, the egg will have been cooking for exactly nine minutes.
PUZZLE #2 SOLUTION
Answer 1: Say "Please point to the village you are from." Regardless of where they are from they will point to the truthful village.
Answer 2: You point to either path and say, "Are you from this village?" If the person answers 'yes' then you are pointing to the truthful village, if they answer 'no' then you are pointing to the lying village.
Answer 3: Ask "Which path would a person from the other village say leads to the truthful (or untruthful) village?" Regardless of whom you speak to the answer will filter through one lie, so if you ask for the truthful village the person will point to the lying village, and vice versa.
To understand, answer these four questions:
- If you point to the truthful village what will a truthful person say in answer to your question?
- If you point to the truthful village what will a untruthful person say in answer to your question?
- If you point to the untruthful village what will a truthful person say in answer to your question?
- If you point to the untruthful village what will a untruthful person say in answer to your question?
Note that in the two cases where the answer is "yes" you are pointing to the truthful village and in the two cases where the answer is "no" you are pointing to the untruthful village. Thus you can tell from the reply to which village you are pointing. You do not have to know to whom you are speaking.
PUZZLE #3 SOLUTION
Their ages are 2, 2, and 9.
From the statement that the product of their ages is 36 the possibilities of the three individual ages are:
1,1,36
1,2,18
1,3,12
1,4,9
1,6,6
2,2,9
2,3,6
3,3,4
From the statement that the sum equals the house number it is possible to eliminate all but two possibilities. The sums of the rest are unique and would allow for an immediate answer. For example if the house number were 16 the ages must be 1, 3, and 12. The two remaining possibilities are 2, 2, and 9; or 1, 6, and 6.
After the clue that the oldest has red hair you can eliminate 1, 6, and 6 because the oldest two have the same age thus there is no oldest son. The only remaining possibility is 2, 2, and 9.
PUZZLE #4 SOLUTION
Answer:
1) 9+8+7+65+4+3+2+1 = 99 -> 7 addition signs.
2) 9+8+7+6+5+43+21 = 99 -> 6 addition signs.
PUZZLE #5 SOLUTION
Answer:
Draw a line starting halfway between the numbers 10 and 11 on the face of the clock to a point halfway between the 2 and the 3.
Draw a line starting halfway between the numbers 8 and 9 on the face of the clock to a point halfway between the 4 and the 5.
You now have three sections of the clock, each with numbers adding up to 26.
PUZZLE #6 SOLUTION
Answer:
9:00 - 70 minutes = 7:50
PUZZLE #7 SOLUTION
Answer:
[(2 * 3 + 8)/2] - 6 = 1 <- NO
[(6 * 3 + 8)/2] - 6 = 7 <- NO
[(8 * 3 + 8)/2] - 6 = 10 <- NO
[(4 * 3 + 8)/2] - 6 = 4 <- YES!! The number is 4
PUZZLE #8 SOLUTION
Rachel
Jane
Kim
Shawn
PUZZLE #9 SOLUTION
Answer:
12 - 7 = 5 people in bare feet!
Socks: 6 Shoes: 4 Socks and Shoes: 3
3 wearing just socks, 1 wearing just shoes, 3 wearing both
3+1+3=7 12 total people - 7 wearing something = 5 barefoot
PUZZLE #10 SOLUTION
Answer:
- 1 and 17 are female -- from clue 1 and 3
- 5 and 7 are male -- from above
- J did not come 3rd -- from clue 5
- 17 is not first -- from clue 1
- Kim is not first.
- Rick finished before 7, therefore he must be 5 after Raelene who was first, therefore,
- Raelene is #1 and first
- Rick is #5 and second
- Kim is #17 and third
- Jim is #7.
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