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The case = of this problem was used by Bjorn Poonen as the opening example in a survey on undecidable problems in number theory, of which Hilbert's tenth problem is the most famous example. [57] Although this particular case has since been resolved, it is unknown whether representing numbers as sums of cubes is decidable.
There seems to be a discrepancy, as there cannot be two answers ($29 and $30) to the math problem. On the one hand it is true that the $25 in the register, the $3 returned to the guests, and the $2 kept by the bellhop add up to $30, but on the other hand, the $27 paid by the guests and the $2 kept by the bellhop add up to only $29.
The digit sum of 2946, for example is 2 + 9 + 4 + 6 = 21. Since 21 = 2946 − 325 × 9, the effect of taking the digit sum of 2946 is to "cast out" 325 lots of 9 from it. If the digit 9 is ignored when summing the digits, the effect is to "cast out" one more 9 to give the result 12.
The problem is so well known that the entire class is often referred to broadly as "monkey and coconut type problems", though most are not closely related to the problem. Another example: "I have a whole number of pounds of cement, I know not how many, but after addition of a ninth and an eleventh, it was partitioned into 3 sacks, each with a ...
The Ages of Three Children puzzle (sometimes referred to as the Census-Taker Problem [1]) is a logical puzzle in number theory which on first inspection seems to have insufficient information to solve. However, with closer examination and persistence by the solver, the question reveals its hidden mathematical clues, especially when the solver ...
In the ray tracing problem for a 3-dimensional system of reflective or refractive objects, determining if a ray beginning at a given position and direction eventually reaches a certain point. [ 15 ] Determining if a particle path of an ideal fluid on a three dimensional domain eventually reaches a certain region in space.
Now that each of the guests has been given $1 back, each has paid $9, and each has an extra, unexpected profit of $1 bringing the total paid to $27 and the total refund to $3. The bellhop has 2 dollars which is subtracted from the total amount paid to the hotel of $27, as this was stolen by the bellhop from the $27 the guests had "paid" to the ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.