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It becomes easier to solve with less calculations required. A reasonable value for u could be u = t·t/4 for the corresponding t based on the largest product of two factors whose sum are t being (t/2)·(t/2). Now the problem has a unique solution in the ranges 47 < t < 60, 71 < t < 80, 107 < t < 128, and 131 < t < 144 and no solution below that ...
First, you have to understand the problem. [2] After understanding, make a plan. [3] Carry out the plan. [4] Look back on your work. [5] How could it be better? If this technique fails, Pólya advises: [6] "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"
Here is a set of four fours solutions for the numbers 0 through 32, using typical rules. Some alternate solutions are listed here, although there are actually many more correct solutions. The entries in blue are those that use four integers 4 (rather than four digits 4) and the basic arithmetic operations. Numbers without blue entries have no ...
On the contrary, many important mathematical results (theorems) are solutions of problems that other mathematicians failed to solve, and the invention of a way for solving them may be a fundamental way of the solving process.
Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle. Conway's Game of Life and fractals , as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions.
When we recently wrote about the toughest math problems that have been solved, we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir ...