The Orange Bag

You wouldn't like to be cheated, or in other words, to not buy a bag below the median weight.

E4
So you're at the grocery store buying a bag of oranges. The oranges are pre-bagged and all the bags are sold at the same price. All the bags have the same number of oranges, but they don't weigh the same. You wouldn't like to be cheated, or in other words, to not buy a bag below the median weight. You begin by grabbing a bag with each hand to compare them. Once you decide on the heavier one you discard the one that feels lighter, keeping the one that feels heavier in your other hand, and pick up another bag with your free hand to make another comparison and continue the process.
Given that you're right about which bag is heavier 90 per cent of the time, and, assuming for simplicity's sake, your chances of misjudging the heavier of two bags are independent of their weight difference, how many bags will you have to pick up to be 85 per cent certain you're not being cheated? (Note: The number of bags to choose from is very large and there are no bags whose weight is equal to the median weight.) 
DEAR MS
(The problem was: "You have four straight pieces of fencing: 1, 2, 3, and 4 metres in length. What's the maximum area you can enclose by connecting the pieces if the land is flat?" - MS) 
What's-In-A-Quad Dept:
The semi-perimeter of the quadrilateral 'S' = (1 + 2 + 3 + 4)/2 = 10/2 = 5m. The maximum area of the quadrilateral land that can be enclosed by connecting the four pieces of fencing, 'A' is given by A^2 = (S-1)(S-2)(S-3)(S-4) = (5-1)(5-2)(5-3)(5-4) = 24. A = (24)^(0.5) = 4.89898, which is 4.9sqm (approximately).
- Dr K N Murty, ?k_n_murty@yahoo.com 
.And then I Googled. Lo and behold, I got the answer. The first link, mathpuzzle.com, said the max area is sqrt(24) or sqrt(1*2*3*4). It was a good read with a reference to Brahmagupta and his theorems.
- Sujit Kumar, ?sujit.iitr@gmail.com 
(The other problem was: "One clue defines the whole word; the other defines the word that is formed when the initial letter of the first word is removed:" - MS) 
D-Ept Dept: 1.?MOST/IN GOOD TIME). 4. E-MOTION (FEELING/MOVEMENT). 5. A-STERN (AFT/SEVERE). 6. U-SURER (MONEY LENDER/MORE CERTAIN). 7. S-IMPLY (WITHOUT DIFFICULTY/SUGGEST). 8. T-ROUBLES (DIFFICULTIES/FOREIGN CURRENCY). 9. E-STRANGE (ALIENATE/ODD). 10. N-EAT (TIDY/DINE).
- Dr A K Bhat, docakbhat@gmail.com
(The third problem was: "If the area and volume of a certain sphere are both four-digit integers times pi, what is the radius of the sphere?" - MS) 
Going-On-17 Dept:
We just need to check out some values of r^2 and r^3 so that the required product is a four-digit number. The value of r can be narrowed down to bigger than or equal to 16 using r^2; and less than or equal to 19 using r^3. The value of the radius that does the job is 18.
- Saifuddin S F Khomosi, ?saif_sfk@hotmail.com 
The area and volume of a sphere that ?has four-digit integers times pi have their radius from 16-19 units. For 16 units, SA = 5461.33p, V = 1024p; 17, SA = 6550.67p, V = 1156p;18, SA = 7776p, V = 1296p; 19, SA = 9145.33p, V = 1444p.
- Jaelyne Tauro, ?jaelynetauro@gmail.com
ENDGAME(S)
(To get in touch with Mukul, mail him at mukul.mindsport@gmail.com) 

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