初中数学竞赛中的整数问题

例1已知自然数A,B和各位数字之和分别为17和11,且A,B两数相加时,仅有一次进位,那么和A+B的各位数字和是多少?这里A,B中较小的数至少是多少?【思路分析】两位数相加时,每进位一次,它们的和的各位数字之和要比这两位数的各位数字的总和减少9.     

Vertex-antimagic labelings of regular graphs

Let G = (V, E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V (G) ∪ E(G) onto the set of consecutive integers 1, 2, . . . , p + q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f (x) assigned to the vertex x together with all values f (xy) assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1, . . . , r + 1.     

利用孪生质数解填数趣题

<正>贵刊在2010年11月的智慧窗中,有一道"和为质数"的趣题:请将5²0分别填入圆圈内,使相邻的两个数之和都是质数,试试看看,你能完成吗?原文中有一个答案,当然正确无误,本文想到用孪生质数:29与31,11与13.为了节省篇幅,可以排成:     

On the longest length of consecutive integers

Choose m numbers from the set {1, 2, …, n} at random without replacement. In this paper we first establish the limiting distribution of the longest length of consecutive integers and then apply the result to test randomness of selecting numbers without replacement.     

浅说幻方

幻方是将1～n2(整数n≥3)这n2个连续整数填入n×n方格中,使得它的每行、每列以及两条对角线上的数字和都相等的数表,其中的n称为"阶".幻方又称"纵横图",也叫"魔方阵",n是几时就叫几阶幻方.例如3阶幻方,4阶幻方,5阶幻方等等.对于幻方,我国宋代著名数学教育家杨辉(1227～1279)曾专门研究过它,下面给出一些简单幻方的制作方法.