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Power digit sum $2^{15} = 32768$ and the sum of its digits is $3 + 2 + 7 + 6 + 8 = 26$. What is the sum of the digits of the number $2^{1000}$? 幂的数字和 阅读全文
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Lattice paths Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bott 阅读全文
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Longest Collatz sequence The following iterative sequence is defined for the set of positive integers: n → n/2 (n is even) n → 3n + 1 (n is odd) Using 阅读全文
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Large sum Work out the first ten digits of the sum of the following one hundred 50 digit numbers. 大和 计算出以下一百个50位数的和的前十位数字。 解题思路 目前想到的就是用高精度加法模拟。 100个5 阅读全文
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Highly divisible triangular number The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 阅读全文
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Largest product in a grid In the 20×20 grid below, four numbers along a diagonal line have been marked in red. 08 02 22 97 38 15 00 40 00 75 04 05 07 阅读全文
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Summation of primes The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. 素数的和 所有小于10的素数的和是2 + 3 + 5 阅读全文