Problem 28: Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:
21 22 23 24 25 20 7 8 9 10 19 6 1 2 11 18 5 4 3 12 17 16 15 14 13
It can be verified that the sum of the numbers on the diagonals is 101.
What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
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Problem 27: Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0 of the form: n² + an + b, where |a| 1000 and |b| 1000,
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Problem 26: Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part. Continued reading >
Problem 25: What is the first term in the Fibonacci sequence to contain 1000 digits?
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Problem 24: What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
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Problem 23: Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
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Problem 22: Using names.txt, a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a name score.
What is the total of all the name scores in the file?
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Problem 21: Evaluate the sum of all amicable pairs under 10000.
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Problem 20: Find the sum of the digits in the number 100!
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Problem 19: How many Sundays fell on the first of the month during the twentieth century?
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