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The Milton Bradley version of Chutes and Ladders has 100 squares, with 19 chutes and ladders. A player will need an average of 39.2 spins to move from the starting point, which is off the board, to square 100. A two-player game is expected to end in 47.76 moves with a 50.9% chance of winning for the first player. [25]
A non-negative integer is a square number when its square root is again an integer. For example, =, so 9 is a square number. A positive integer that has no square divisors except 1 is called square-free. For a non-negative integer n, the n th square number is n 2, with 0 2 = 0 being the zeroth one. The concept of square can be extended to some ...
Many of the numbers have styles and personalities associated with their numbers (One is brave and independent, Four loves squares as he is a square number, Seven is rainbow-coloured and lucky due to the superstition behind that number, Eight has octopus-like tentacles as octopuses have 8 tentacles, Eleven loves football as a football team has ...
The numbers are based on a $50 a square game, with a $625 payout for the 1st and 3rd quarters, a $1,250 payout for halftime, and a $2,500 payout for the end of the game. (The cells are colored ...
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All centered square numbers and their divisors have a remainder of 1 when divided by 4. Hence all centered square numbers and their divisors end with digit 1 or 5 in base 6, 8, and 12. Every centered square number except 1 is the hypotenuse of a Pythagorean triple (3-4-5, 5-12-13, 7-24-25, ...). This is exactly the sequence of Pythagorean ...
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Consequently, a square number is also triangular if and only if + is square, that is, there are numbers and such that =. This is an instance of the Pell equation x 2 − n y 2 = 1 {\displaystyle x^{2}-ny^{2}=1} with n = 8 {\displaystyle n=8} .
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