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코딩 연습
In a\(3 \times 2\) cross-hatched grid, a total of \(37\) different rectangles could be situated withing that grid as indicated in the sketch. There are \(5\) grids smaller than \(3 \times 2\), vertical and horizontal dimensions being important, i.e. \(1 \times 1\), \(2 \times 1\), \(3 \times 1\), \(1 \times 2\) and \(2 \times 2\). If each of them is cross-hatched, the following number of differe..
The smallest positive integer \(n\) for which the numbers \(n^2 +1\), \(n^2 +3\), \(n^2+7\), \(n^2+9\), \(n^2+13\), and \(n^2+27\) are consecutive primes is \(10\). The sum of all such integers \(n\) below one-million is \(1242490\). What is the sum of all such integers \(n\) below \(150\) million? \(n^2 +1\), \(n^2 +3\), \(n^2+7\), \(n^2+9\), \(n^2+13\), \(n^2+27\) 이 연속적인 소수가 되는 최소의 자연수 \(n\) 은..
Some positive integers \(n\) have the property that the sum \([n+{\rm reverse}(n)]\) consists entirely of odd (decimal) digits. For instance, \(36+63=99\) and \(409+904=1313\). We will call such numbers reversible; so \(36, \; 63, \; 409\), and \(904\) are reversible. Leading zeroes are not allowed in either \(n\) or \({\rm reverse}(n)\). There are \(120\) reversible numbers below on-thousand. H..