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I think someone has an issue with me. I have been working hard to keep the forum questions alive but someone or maybe several people have gone through and have marked down every entry i have posted. This upsets me and makes me not want to continue participating here.

If three circles are mutually tangent where one has a radius of 3cm, another has a radius of 4cm, and the last has a radius of 5cm. What is the area of the region bounded between the three circles?

List out the numbers from 1 to 150 in a vertical column. Left align all of the numbers to where the leading digit of the number is directly on top of the next number's leading digit (e.g. for the numbers 9, 10, and 11. 9 would be above 1 and that above 1 where zero would have nothing above it and 1 below it ex. ... 9 10 11 ... ) remove the nothing space above all the numbers to where the numbers are shifted up until they are at the top creating a list of new numbers. With this new list of numbers what is the probability of randomly selecting 322? 99? and 140?

Every day, Ellie takes the commuter train and arrives at the station 8:30 AM, where she's immediately picked up by a car and driven to work. One day she takes the early train, arrives at the station at 7:00 AM, and begins to walk towards work. The car picks her up along the way and she gets to work 10 minutes earlier than usual. When did Ellie meet the car on this day?

A reporter on New Year's Eve 1993 wanted to know, from Pat and Chris, how old they were, but felt (correctly, it turns out) that one would lie. So the reporter asked them both, "Write down your age now, your age at the end of next year, add these together, then multiply the result by 5," quickly followed by: "now add the last digit of the year you were born." They had no time to fake that last digit; Pat answered 281, while Chris announced 229. Who was lying, and what were their real ages at the time?

What is the maximum number of Friday-the-13ths that there can be in a single year? What is the minimum number?

From now on, the "+" symbol no longer means to combine the count of objects (e.g. 3 things plus 4 things make 7 total things would not be modeled as 3 + 4 = 7). Instead, the use of the + symbol is to show 5 + 3 = 7 to resolve the question of "how many spaces between objects are created when you line up five things and three things" (ex: t _ t _ t _ t _ t _ t _ t _ t ) and this is now to be considered addition If the other basic computational symbols maintained the same relationship to addition as they had before this new convention what would be the answers to the following problems? 4 - 3 = ? 3 x 3 = ? 9 / 3 = ? sqrt (36) = ?

The people living on Sesame Street all decide to buy new house numbers, so they line up at the store in order of their addresses: 1, 2, 3, . . . . If the store has 100 of each digit, what is the first address that won't be able to buy its house numbers?

Winoc sells four types of products. The resources needed to produce one unit of each and the sales prices is listed below: Resource Product 1 Product 2 Product 3 Product 4 Raw Material 2 3 4 7 Hours of labor 3 4 5 6 Sales Price ($) 4 6 7 8 Currently, 4,600 units of raw material and 5,000 labor hours are available.To meet customer demands, exactly 950 total units must be produced. Customers also demand that at least 400 units of product 4 be produced. What is the solution that maximizes Winoc's sales revenue?

suppose there is a three digit number M where 100*a + 10*b +1*c = M where a, b, and c are digits What is the minimum value that can be found from M/(a+b+c)?

Many of my algebra and precalculus students think the 'inverse function' of f(x), often written f^(-1)(x), is the same as the reciprocal 1/f(x) (mistaking the -1 for an exponent). This (as I am obliged to remind them) is almost always false. But can you find at least one function whose inverse is also its reciprocal? Tiebreaker: Find as many as you can!

Two circles are drawn with five inches between the centers. A line is drawn tangent to the bottom of one circle and the top of the other. The circumference of one circle is 6.28 inches. The area of the other circle is 12.56 inches squared, Angle x is formed by the tangent line and the line between the centers. Determine angle x. (assume that pi = 3.14)

You have an old-fashioned refrigerator with a small freezer compartment capable of holding seven ice cube trays stacked vertically. But there are no shelves to separate the trays, and if you stack one tray on top of another before the ice cubes in the bottom tray are fully frozen, the top tray will nestle into it, and you won't get full cubes in the bottom tray. You have an unlimited supply of trays, each of which can make a dozen cubes. What's the fastest way to make full-sized ice cubes?

Two players play the following game with a fair coin. Player 1 chooses (and announces) a triplet (HHH, HHT, HTH, HTT, THH, THT, TTH, or TTT) that might result from three successive tosses of the coin. Player 2 then chooses a different triplet. The players toss the coin until one of the two named triplets appears. The triplets may appear in any three consecutive tosses: (1st, 2nd, 3rd), (2nd, 3rd, 4th), and so on. The winner is the player whose triplet appears first. What is the optimal strategy for each player? With best play, who is most likely to win? Suppose the triplets were chosen in secret? What then would be the optimal strategy? What would be the optimal strategy against a randomly selected triplet?

I have lots of photo prints, in two sizes: (a) 4 x 6 inches, and (b) 5 x 7 inches. I put photos up on the wall, each one can be vertical or horizontal, so that they tile into a big rectangle (with no overlapping or cutting, of course). i) Prove I can't make a 19 x 19-inch "photo-square." II) Show me how to tile the 29 x 29 photo-square.

PowerCo has three plants that must provide enough electricity to four cities. Shipping to each city from the various plants costs varying amounts. Moreover each plant has a set supply of energy that it can send to the various cities. The specifics of this information are outlined in the chart below: From City 1 City 2 city 3 city 4 Supply Plant 1 $8 $6 $10 $9 35 Plant 2 $9 $12 $13 $7 50 Plant 3 $14 $9 $16 $5 40 Demand 45 20 30 30 How can PowerCo best minimize its costs?

As a swimmer jumps off a small bridge and begins to swim upstream, her swim cap comes off and floats downstream. Ten minutes later she turns around, swimming downstream with the same effort, past her original bridge. At the next bridge, 1000 meters away from the first, she catches the cap. What was the speed of the current? Of the swimmer?

a b and c are digits not integers, good idea though. If they were integers there would still be smaller answer then what you have found here. can you find that answer too? I disagree with your first solution (well) since it is undefined, we don't know if the value is defined to mean min or max as it is undefined

i found an error in my calculation using 189/18 = 10.5 oops nice work!

Prem was doing his homework. With a radius of 20cm he drew a circle. He then drew 7 lines inside the circle with the help of a foot-rule. Can you tell in how many minimum and maximum divisions was the circle divided by these lines?

Tommy muttonhead propounds to his teacher the perplexing query: "If five times six were 33, what would the half of 20 be?" The other pupils solved the problem redily, but Tommy could not see how a thing that was not what they said it was had anything to do with something else that is not what they say it is.

Daddy came back from the market. He purchased two hammers. Dad said that the hammer was either $1.50 for one or $2.50 for two but either way the vendor was to make the same profit either way. How is this possible?

I think one of the problems with this problem is that we are missing the assumption that standard ice trays hold 12 ice cubes

When Jack went back for a late-night snack, he bought three items off the rack. Zack rang up the snacks and said "5.70, Jack." "Wait, Zack, you multiplied the prices instead of adding!" "Multiply, add; it still comes out the same. Pay up." What were the prices of Jack's three items?

King Chester awarded a triangular piece of land to his favorite court jester. The three sides measured 150 2/3 yards, 195 3/4 yards, and 45 yards 3 inches. His wife had long been asking him to have a piece of land where she could build a home, a garden, and a temple in each corner. The jester told his wife the good news but was surprised that shew as unhappy. Can you tell why she was unhappy?

Steelco has received an order for 100 tons of steel. The order must contain at least 3.5 tons of nickel, at most 3 tons of carbon, and exactly 4 tons of manganese. Steelco receives $20/ton for the order. To fill the order, Steelco can combine four alloys, whose chemical composition and cost is given in the table below: Alloy (%) Content 1 2 3 4 Nickel 6 3 2 1 Carbon 3 2 5 6 Manganese 8 3 2 1 Cost/Ton ($) 12 10 8 6 Steelco wants to optimize profit (revenue-costs) obtained from filling the order. How much of each Alloy content type must they produce to achieve optimal profit?

"What time is it, Rory?" asked Cory one lazy day. "When I checked my watch this morning, the hour hand was where the minute hand is now, and the minute hand was one minute before where the hour hand now sits. I notice both hands are now at exact minute divisions." What is the time now? When did Rory check this morning?

The product, the quotient, and the difference of two real numbers are all the same. Find the sum of the two numbers.

Resource Desk Table Chair Availability Lumber 8 board ft 6 board ft 1 board ft 48 board ft Finishing 4 hours 2 hours 1.5 hours 20 hours Carpentry 2 hours 1.5 hours 0.5 hours 8 hours Selling Price $60 $30 $20 Given the constraints listed in terms of time and wood available, how many of each object should be produced to maximize revenue?

18,8,21,24 22,24 2,1,1,25, 4,17,25 8 3,8,13,13 13,8,21,24; 18,8,21,24 22,24 3,4,9,24,10, 4,17,25, 8 3,8,13,13 25,8,24. 3,12,4,9 4,22 8? The large punctuation is meant to be maintained when you resolve this cryptogram. The small commas is only meant to separate the numbers they go together as a single word. Like last time, i don't care if you can translate this cryptogram. I want the correct answer in code.

I like your answer. It is interesting how in America this problem is solved differently from my home country. I'm intrigued. How do people from your country solve this problem?

Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project. Together, A, B, and C can complete it in 10 days. Together, B, C, and D can complete it in 11 days. Together, C, D, and A can complete it in 12 days. Together, D, A, and B can complete it in 13 days. Who is the best performer? Prove your answer.

Verdict Is Guilty Verdict is not Guilty Committed Crime 80% 20% False Negative Innocent of Crime 10% False Positive 90% The above chart shows the rate that individuals are correctly found guilty or innocent of crimes in a particular jurisdiction. If 1% of the population of residents in this county were tried in court, what are the chances that someone was correctly charged with crime?

The school children were returning to their homes when they met the mathematical milkman, who propounds the following problem: In one of the two cans there is milk which is so rich with cream that it becomes absolutely necessary to dilute it with a little water to make it wholesome. Therefore, in the other can there is some pure spring water, now I proceed to pour spring water from can No. 1 into can No. 2 sufficient to double its contents, and then repour from No. 2 into No.1 enough of the mixture to double the contents. Then to equalize matters, I again pour from No. 1 into No. 2 to double the contents of No. 2 and find the same number of gallons of milk in each can, although there is one more gallon of water in can No. 2 than there is milk, so I want you to tell me how much more water than milk is there in can No. 1?

Are you saying what is the greatest path?

You and your spouse invite four other couples to a party. During the course of the conversation, it is discovered that, prior to the party, each person except you was acquainted with a different number of the people present. Assuming the acquaintance relationship is symmetric (i.e., if you are acquainted with someone, that person is also acquainted with you), then how many people did your spouse know prior to the party? How many people did you know?

TPVM YXKD WL VJB BXTJ MPK DMVEID TEMPXWM NXUEJY? I don't care if you can translate the cryptogram. I want to know if you can solve the question.

Reason why 30414093201713378043612608166064768844377641568960512078291027000 cannot possibly be the value of 50 factorial, without actually performing the calculation.

You've been sentenced to death in an obscure foreign country which has a strange law. Before the sentence is carried out, two papers -- one with "LIFE" written on it and one with "DEATH" written on it -- are folded up and placed in a hat. You are permitted to pick out one of the papers (without looking), and if you choose the one with "LIFE" written on it, you are set free. Otherwise, the death sentence is carried out. On this occasion, a mean-spirited acquaintance of yours, bent on your demise, has substituted the paper with "LIFE" written on it with another one with "DEATH" written on it. This person gleefully informs you of what he has done and that you are doomed to die. You are not permitted to speak to anyone about this misdeed, nor will you have a chance to switch the papers or the hat yourself in time. How will you avoid certain death?

In a rectangular array of people, who will be taller: the tallest of the shortest people in each column, or the shortest of the tallest people in each row?

How can you build pig pens so you can put nine pigs in four pens such that each pen has an odd number of pigs?

Two days ago, Suzy was 8. Next year, she'll be 11. How is this possible?

An Arab sheikh is old and must will his fortune to one of his two sons. He makes a proposition. His two sons will ride their camels in a race, and whichever camel crosses the finish line last will win the fortune for its owner. During the race, the two brothers wander aimlessly for days, neither willing to cross the finish line. In desperation, they ask a wise man for advice. He tells them something; then the brothers leap onto the camels and charge toward the finish line. What did the wise man say?

2^3=3^1+5 2^5=3^3+5

You own a pet store. If you put in one canary per cage, you have one canary too many. If you put in two canaries per cage, you have one cage too many. How many canaries and cages do you have?