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8) 9 + 9 + 9 -2 = 25 + 2 -2 (adding -2 to both sides of the equation to cancel the +2 on the right side, which means the bellhop returned the tip or gave a discount of $2) 9) 9 + 9 + 9 - 2 = 25 10) 27 - 2 = 25 11) 25 = 25. The puzzle should subtract the bellhop's tip from the $27 rather than add it. History. There are many variants of the puzzle.
Weakly prime numbers. Primes that having any one of their (base 10) digits changed to any other value will always result in a composite number. 294001, 505447, 584141, 604171, 971767, 1062599, 1282529, 1524181, 2017963, 2474431, 2690201, 3085553, 3326489, 4393139 ( OEIS : A050249 )
In mathematics, Apéry's constant is the sum of the reciprocals of the positive cubes. That is, it is defined as the number. where ζ is the Riemann zeta function. It has an approximate value of [1] ζ(3) ≈ 1.20205 69031 59594 28539 97381 61511 44999 07649 86292 … (sequence A002117 in the OEIS ). The constant is named after Roger Apéry.
The unary numeral system is the simplest numeral system to represent natural numbers: to represent a number N, a symbol representing 1 is repeated N times. [2] In the unary system, the number 0 (zero) is represented by the empty string , that is, the absence of a symbol.
It is known that ζ(3) is irrational (Apéry's theorem) and that infinitely many of the numbers ζ(2n + 1) : n ∈ , are irrational. There are also results on the irrationality of values of the Riemann zeta function at the elements of certain subsets of the positive odd integers; for example, at least one of ζ (5), ζ (7), ζ (9), or ζ (11 ...
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
855 = 3 2 × 5 × 19, decagonal number, centered cube number. country calling code for Cambodia; 856 = 2 3 × 107, nonagonal number, centered pentagonal number, happy number, refactorable number. country calling code for Laos; 857 = prime number, sum of three consecutive primes (281 + 283 + 293), Chen prime, Eisenstein prime with no imaginary part
168 is also coefficient four in the expansion of Eisenstein series, which also includes 144 and 96 (or 48 × 2) as the fifth and third coefficients, respectively — these have a sum of 240, which follows 144 and 187 in the list of successive composites (+) = (); cf. the latter holds a sum-of-divisors of 216 = 6 3, which is the 168th composite ...