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Guest Message by DevFuse


Member Since 18 Feb 2013
Offline Last Active Yesterday, 02:06 PM

#332401 Coin Triplets

Posted by BMAD on 20 May 2013 - 10:49 PM

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?

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#332388 How Low can U go?

Posted by BMAD on 20 May 2013 - 07:19 PM

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)?

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#332387 At the Snack Shack

Posted by BMAD on 20 May 2013 - 07:14 PM

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?

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#332386 A swimmer loses their cap.

Posted by BMAD on 20 May 2013 - 07:09 PM

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?

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#332384 Ridiculous Inverse

Posted by BMAD on 20 May 2013 - 07:04 PM

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!

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#332378 An ungrateful award

Posted by BMAD on 20 May 2013 - 04:36 PM

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?

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#332377 Breaking through the circle

Posted by BMAD on 20 May 2013 - 04:18 PM

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?

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#332367 PowerCo

Posted by BMAD on 20 May 2013 - 05:21 AM

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?

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#332339 What time is it?

Posted by BMAD on 19 May 2013 - 02:28 AM

"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?

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#332338 Tessellated Pictures

Posted by BMAD on 19 May 2013 - 02:24 AM

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.

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#332337 Two special numbers

Posted by BMAD on 19 May 2013 - 02:22 AM

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

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#332316 Winoc Sells

Posted by BMAD on 17 May 2013 - 11:55 PM

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?

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#332280 The Best Performer

Posted by BMAD on 17 May 2013 - 04:32 AM



Let a, b, c, and d stand for the fraction of a project that A, B, C, and D can do within each day, respectively.
Spoiler for


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?




brainden worker performance.png

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#332260 Whether to produce desks, tables, or chairs

Posted by BMAD on 17 May 2013 - 02:49 AM

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?

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#332256 SteelCo

Posted by BMAD on 17 May 2013 - 02:38 AM

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?

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