 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
c# qr code generator Inside Microsoft SQL Server 2008: TSQL Querying in Visual C#
Inside Microsoft SQL Server 2008: TSQL Querying Print QR Code 2d Barcode In C#.NET Using Barcode creator for Visual Studio .NET Control to generate, create QR Code ISO/IEC18004 image in .NET framework applications. www.OnBarcode.comQR Code Decoder In C#.NET Using Barcode scanner for VS .NET Control to read, scan read, scan image in .NET applications. www.OnBarcode.comOf course, this is just an observation of a pattern based on the cases that were tested. To ensure that the pattern holds for all cases, you need a mathematical proof. You can nd one at http://en.wikipedia.org/wiki/Josephus_problem. The following TSQL statement calculates and returns p for a given @n: Creating Barcode In C#.NET Using Barcode encoder for .NET framework Control to generate, create barcode image in .NET applications. www.OnBarcode.comReading Barcode In C# Using Barcode reader for .NET framework Control to read, scan read, scan image in .NET applications. www.OnBarcode.comDECLARE @n AS INT = 41; SELECT 2 * (@n  POWER(2, CAST(LOG(@n)/LOG(2) AS INT))) + 1 AS p; Painting QR Code In Visual Studio .NET Using Barcode creation for ASP.NET Control to generate, create QR Code image in ASP.NET applications. www.OnBarcode.comQR Code Drawer In .NET Using Barcode creation for Visual Studio .NET Control to generate, create QR Code JIS X 0510 image in Visual Studio .NET applications. www.OnBarcode.comPuzzle 23: Shipping Algebra
Quick Response Code Creator In VB.NET Using Barcode creator for .NET Control to generate, create QR Code 2d barcode image in Visual Studio .NET applications. www.OnBarcode.comMatrix Barcode Drawer In Visual C#.NET Using Barcode drawer for .NET Control to generate, create Matrix Barcode image in VS .NET applications. www.OnBarcode.comHere s the algebra I used in my solution to the problem: Let s = current age of ship, b = current age of boiler, and y = years passed since the age of the ship was equal to the current age of the boiler. You can translate the statements in the puzzle to the following three equations: 1. s + b = 42 2. s = 2 (b y) 3. s y = b From equations 2 and 3 you get the following equation: s = 2 (b s + b) This gives us equation 4: 4. 3 s = 4 b From equations 1 and 4 you get the following equation: 3 s = 4 (42 s) When you solve the equation for s, you get 24. And now that the age of the ship is known, you can solve equation 1 for b: b = 42 24 = 18 The solution is that the ship s current age is 24 and the boiler s current age is 18. Printing 1D In Visual C#.NET Using Barcode creation for VS .NET Control to generate, create Linear Barcode image in VS .NET applications. www.OnBarcode.comBar Code Drawer In Visual C# Using Barcode generator for Visual Studio .NET Control to generate, create bar code image in VS .NET applications. www.OnBarcode.comPuzzle 24: Equilateral Triangles Puzzle
Painting UPCA In Visual C# Using Barcode drawer for Visual Studio .NET Control to generate, create UCC  12 image in .NET applications. www.OnBarcode.comCode 11 Encoder In Visual C#.NET Using Barcode printer for VS .NET Control to generate, create Code11 image in .NET applications. www.OnBarcode.comYou can solve this puzzle in many ways. I provided this puzzle not because it is tough but rather the contrary it is pretty simple. However, some of the solutions are simply beautiful. I ll rst provide an ordinary solution and then a more creative one. To explain the rst solution, examine the drawing in Figure A4. Barcode Creation In Java Using Barcode generation for Android Control to generate, create bar code image in Android applications. www.OnBarcode.comDataMatrix Drawer In Java Using Barcode generator for BIRT reports Control to generate, create Data Matrix 2d barcode image in BIRT reports applications. www.OnBarcode.comAppendix A E
Printing QR Code 2d Barcode In Java Using Barcode drawer for Java Control to generate, create QR Code JIS X 0510 image in Java applications. www.OnBarcode.comBarcode Decoder In VB.NET Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in Visual Studio .NET applications. www.OnBarcode.comLogic Puzzles
Reading Barcode In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. www.OnBarcode.comUPC Code Scanner In VB.NET Using Barcode decoder for VS .NET Control to read, scan read, scan image in .NET framework applications. www.OnBarcode.comh2 a
Generate Barcode In .NET Using Barcode generator for .NET Control to generate, create bar code image in Visual Studio .NET applications. www.OnBarcode.comCreating Bar Code In .NET Using Barcode encoder for .NET framework Control to generate, create barcode image in .NET applications. www.OnBarcode.comS A F C G H
FIGURE A4 Solution 1 to the equilateral triangles puzzle
The segment h1 has the same length as the altitude of the triangle ABC, and the segment h2 has the same length as the altitude of the triangle CEF. G is the point where h1 intersects CA, and H is the point where h2 intersects the same line. It is fairly easy to prove that H is the same point as A but not really necessary for our purposes. The triangles GBC and HEC are similar because they have two corresponding angles that are equal (both have a right angle and share another angle). CE is twice CB; therefore HE (which is h2) is twice GB (which is h1). The area of a triangle is bh (half base times altitude). Because the bases FC and CH of the triangles CEF and ABC have equal lengths but h2 is twice h1, the area of CEF is twice the area of ABC. In other words, the area of CEF (as well as DEB and DAF, which are congruent to CEF) is 2S. Therefore, the area of the triangle DEF is 3 2S + S = 7S. The second solution is more creative. Examine the drawing in Figure A5. You draw the lines EG and GF parallel to CF and EC, respectively, to form the parallelogram CEGF. Next, draw the lines BG, BH, and CE. We know that FC = CB = BE = EG = GH = HF = HB = a. Triangles ABC, CHF, and BGH are congruent because corresponding sides and the angle between them are equal. This means that HC = BG = a. This means that the four triangles BEG, BGH, CBH, and CHF enclosed by the parallelogram and ABC are congruent; therefore, the area of the parallelogram is 4S. The triangle CEF has exactly half the area of the parallelogram; therefore, the triangle s area is 2S. Therefore, the area of the triangle DEF is 3 2S + S = 7S.

