I was talking to a colleague the other day about HTML5-Snake, and somehow the conversation drifted to Pacman…
After a weekend of investigating the Pacman (enemy) strategies, I took a break from doing EulerProject questions and began work on it.
It seemed simple enough: the background was pre-made, (sprites were handmade), and it seemed very do-able.
It took me 2 days for the base code, +1 for memory/cpu profiling.
It is without sound, but I think it’s quite playable.
You can try it out here.
Problem 68:
Consider the following “magic” 3-gon ring, filled with the numbers 1 to 6, and each line adding to nine.
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Problem 66:
Consider quadratic Diophantine equations of the form:
Problem 65:
The square root of 2 can be written as an infinite continued fraction.
sqrt(2) = 1+1/(2+(1/(2+1/(2+1/…))))
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Problem 64:
The first ten continued fraction representations of (irrational) square roots are:
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Problem 63:
The 5-digit number, 16807=7^5, is also a fifth power. Similarly, the 9-digit number, 134217728=8^9, is a ninth power.
How many n-digit positive integers exist which are also an nth power?
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Problem 62:
The cube, 41063625 (345^3), can be permuted to produce two other cubes: 56623104 (384^3) and 66430125 (405^3).
In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube.
Find the smallest cube for which exactly five permutations of its digits are cube.
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Problem 61:
Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae:
Triangle P3,n=n(n+1)/2 1, 3, 6, 10, 15, ... Square P4,n=n2 1, 4, 9, 16, 25, ... Pentagonal P5,n=n(3n-1)/2 1, 5, 12, 22, 35, ... Hexagonal P6,n=n(2n-1) 1, 6, 15, 28, 45, ... Heptagonal P7,n=n(5n-3)/2 1, 7, 18, 34, 55, ... Octagonal P8,n=n(3n-2) 1, 8, 21, 40, 65, ...
The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties.
The set is cyclic, in that the last two digits of each number is the first two digits of the next number (including the last number with the first).
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Problem 60:
The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime.
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Problem 59:
The encryption key consists of three lower case characters. Using cipher1.txt, a file containing the encrypted ASCII codes, and the knowledge that the plain text must contain common English words, decrypt the message and find the sum of the ASCII values in the original text.
Note that the key is repeated cyclically throughout the message utilizing XOR.
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