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For =, Selfridge–Conway procedure solves the problem in finite time with 5 cuts (and at most 2 pieces per agent). For , the Aziz-Mackenzie procedure solves the problem in finite time, but with many cuts (and many pieces per agent).
The proof was accepted for publication in the Annals of Mathematics Studies series [3] in 2015, and has been undergoing further review and revision since; fully-refereed chapters in close to final form are being made public in the process. [4] Some state the conjecture as Every odd number greater than 7 can be expressed as the sum of three odd ...
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.
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.
Frobenius coin problem with 2-pence and 5-pence coins visualised as graphs: Sloping lines denote graphs of 2x+5y=n where n is the total in pence, and x and y are the non-negative number of 2p and 5p coins, respectively. A point on a line gives a combination of 2p and 5p for its given total (green).
For example, for 2 5 a + 1 there are 3 increases as 1 iterates to 2, 1, 2, 1, and finally to 2 so the result is 3 3 a + 2; for 2 2 a + 1 there is only 1 increase as 1 rises to 2 and falls to 1 so the result is 3a + 1.
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.
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 ...