If a bear walks one mile south, turns left and walks one mile to the east and then turns left again and walks one mile north and arrives at its original position, what is the color of the bear?
What the heck?!? Color of the bear? But if you look further into the deep recesses of the question, you might realize that the color of the bear is trivial. There are possible solutions that could be interesting, however. In addition to the north pole, there is also the south pole with additional climate circles close by. Maybe now the bear could be white, brown, who knows. Just make sure your can substantiate your story.
So your child is celebrating their birthday and you go to get the cake. Mysteriously there is one rectangular piece missing. You want to cut the cake in exactly half to freeze half, but use the other half for the party. What do you do? If you are like me, you just grab a knife and make a guess, but that is not the correct answer!
What you do is join the centers of the original and the removed rectangle. Then cut in a straight line from side to side. The cake will be perfectly divided!
Your best friend brings you three baskets of fruit. (The baskets are covered up.) One of them has apples in it, one has oranges, and one is a mixture of apples and oranges. You notice that each basket is labeled, however your friend tells you that as joke the labels lie. (So the basket labeled ORANGES most certainly doesn't have oranges in it, or could be a mixture.) He will allow you to uncover one basket to see what fruit is in it. The task is to pick only one fruit from it and then correctly label all three baskets. If you do so, your friend will give them to you. What do you do?
Since there are only two combination's of distributions in which all the baskets have wrong labels. By picking a fruit from the one labeled MIXTURE, it is possible to tell what the other two baskets have. So, if the fruit in the MIXTURE is an orange, then we know that basket has oranges in it. Apples will be in the basket marked ORANGES and the one marked APPLES will have the fruit mixture.
You have 8 balls. They all look alike, maybe they are all white pool cue balls? One of them is defective and weighs more than the others. You have a balance to measure the balls against each other. In two weighings how do you find the defective one?
Choose 6 balls and weigh 3 against 3. If they weigh the same, you have another weighing for the remaining 2 balls and you can find the heavier one. If they don't weigh the same, from the group of 3 which was heavier, choose any 2 balls and weigh them. If they weigh the same, the remaining ball is the heavier one, otherwise you just found the heavier one by weighing the 2 chosen balls.
You have just invited your cousin Cheko to come and work for you. You work it out with him to work for seven days, agreeing to pay him a gold bar each day. The gold bar is segmented into seven connected pieces. You must give Cheko a piece of gold at the end of every day. If you are only allowed to make two breaks in the gold bar, how do you pay Cheko?
Here is how you do it and keep your end of the deal too! Break 1 piece and 2 pieces, leaving 4 remaining pieces. Do the following each day:
Day 1 - pay 1 piece (1 total piece)
Day 2 - take back 1 piece an give 2 piece(2 total pieces)
Day 3 - pay 1 piece (3 total pieces)
Day 4 - take back 1 and 2 pieces and give 4 piece (total 4 pieces)
Day 5 - give back 1 piece (total 5 pieces)
Day 6 - take back 1 piece and give 2 piece (total 6 pieces)
Day 7 - give back 1 piece (total 7 pieces)
One train leaves Los Angeles at 15mph heading for New York. Another train leaves from New York at 20mph heading for Los Angels on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?
The answer isn't as bad as it may seem. You need to setup an algebraic equation and make an assumption of how many miles it is from New York to Los Angeles, lets say 2800 miles.
Train 1 = 15*T
Train 2 = 20*T
Combine terms:
15*T + 20*T = 2800 miles
35T = 2800 miles
T = 80 hours
So now you know how long it will take before the trains collide, but what about the bird?
Quite simply put, the bird needs to fly 80 hours, and at 25mph,
80 * 25 = 2000 miles
Here is a good on that you can do with all the leftover medical drugs in your medicine cabinet. You have 5 jars of pills. Each pill weighs 10 grams, except for contaminated pills contained in one jar, where each pill weighs 9 grams. Given a scale, how could you tell which jar had the contaminated pills in just one measurement?
Answer:
1. Mark the jars with numbers 1, 2, 3, 4, and 5.
2. Take 1 pill from jar 1, take 2 pills from jar 2, take 3 pills from jar 3, take 4 pills from jar 4 and take 5 pills from jar 5.
3. Put all of them on the scale at once and take the measurement.
4. Now, subtract the measurement from 150 - ( 1*10 + 2*10 + 3*10 + 4*10 + 5*10)
5. The result will give you the jar number which has contaminated pill.
2. Take 1 pill from jar 1, take 2 pills from jar 2, take 3 pills from jar 3, take 4 pills from jar 4 and take 5 pills from jar 5.
3. Put all of them on the scale at once and take the measurement.
4. Now, subtract the measurement from 150 - ( 1*10 + 2*10 + 3*10 + 4*10 + 5*10)
5. The result will give you the jar number which has contaminated pill.
If you have an infinite supply of water and a 5 quart and 3 quart pail, how would you measure exactly 4 quarts?
This is how you could do it:
1. Fill the 5 quart pail.
2. Fill the 3 quart pail from the five quart pail leaving 2 quarts in the 5 quart pail.
3. Empty the 3 quart pail and fill with 2 quarts water water in 5 quart pail.
4. Fill 5 quart pail.
5. Pour water from the 5 quart pail until you fill the 3 quart pail, leaving 4 quarts water in the 5 quart pail.
Last one for today. Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for 17 minutes. The bridge is too dangerous to cross without a flashlight, and it's only strong enough to support 2 people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?
Here is the answer:
A = 1 minute
B = 2 minutes
C = 5 minutes
D = 10 minutes
A (with flash light) and B cross first = 2 minutes
A (with flash light) comes back = 3 minutes
C (with flash light) and D cross = 13 minutes
B (with flash light) comes back = 15 minutes
A and B (with flash light) cross = 17 minutes
Had enough fun for one day?
Till next time,
Bill
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