M 15 数阵图

庄老师 018-3801692 奥林匹克数学 Math Olympiad

Name:________________ Date:____________

数阵图

1. 将 2 到 9 分别填入下图的空格中，使每条边上的三个数之和都等于 18。
Fill in the blanks in the figure below with 2 to 9 respectively, so that the sum of
the three numbers on each side is equal to 18.

2. 把 1 到 8 分别填入小圈圈内，使每个圆周上的五个数之和都等于 21。
Fill in the blanks in the figure below with 1 to 8 respectively, so that the sum of
the five numbers on each circle is equal to 21.

3. 把 1 到 6 这六个自然数分别填入下面三角形的六个圆中，使每条边上三个数
的和相等。

Fill in the blanks in the figure below with 1 to 6 respectively, so that the sum of
the three numbers on each side is equal.

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庄老师 018-3801692 奥林匹克数学 Math Olympiad

4. 将 1 到 9 分别填在下图的圆圈中，要求三条边上四个数的和都相等。
Fill in the blanks in the figure below with 1 to 9 respectively, so that the sum of
the three numbers on each side is equal.

5. 将 6，7，8 三个数（可重复使用）填在下图圆圈中，使每个三角形三个顶点
上的三个数的和都相等。

Fill the three numbers 6,7, and 8(reusable) in the circle in the figure below, so
that the sum of the three numbers on the three vertices of each triangle is equal.

6. 将 1 到 7 这七个数字填入下面的圈圈里，使每条线及每个圈上的三个数的和
相等。

Fill in the blanks in the figure below with 1 to 7 respectively, so that the sum of
the three numbers on each line and each circle is equal.

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庄老师 018-3801692 奥林匹克数学 Math Olympiad

7. 把 1 到 10 这十个自然数分别填入右图，使从三角形中心出发的每条线上的
四个数之和都是 19，每个正三角形三个顶点上的三个数之和都是 18。
Fill in the blanks in the figure below with 1 to 10 respectively, so that the sum of
the four numbers on each line starting from the center of the triangle is 19, and
the sum of the three numbers on the three vertices of each regular triangle is 18.

8. 将下表 3x3 的数格填入 1 到 9，使每行、每列及对角线的和都相等。
Fill in the number from 1 to 9 in the table of 3x3 below so that the sum of each
row, column and diagonal is equal.

9. 将下表 3 x 3 的数格填入 31 到 39，使每行、每列及对角线的和都相等。
Fill in the number from 31 to 39 in the table of 3x3 below so that the sum of each
row, column and diagonal is equal.

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庄老师 018-3801692 奥林匹克数学 Math Olympiad

10. 将下表 3 x 3 的数格填入 54 到 62，使每行、每列及对角线的和都相等。
Fill in the number from 54 to 62 in the table of 3x3 below so that the sum of each
row, column and diagonal is equal.

11. 将下表 4 x 4 的数格填入 31 到 46，使每行及每列的和都相等。
Fill in the number from 31 to 46 in the table of 4x4 below so that the sum of each
row and column is equal.

12. 将下表 4x4 的数格填入 23 到 38，使每行及每列的和都相等。
Fill in the number from 23 to 38 in the table of 4x4 below so that the sum of each
row and column is equal.

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庄老师 018-3801692 奥林匹克数学 Math Olympiad

13. 下表是一个 4 x 4 的数格，请你将下表填写完整，使每行、每列及每条对角
线中都含有 1、2、3、4 这 4 个数字。
The following table is a 4x4 number grid. Please fill in the following table so that
each row, column and diagonal line contains the 4 numbers 1, 2, 3 and 4.

14. 下表是一个 5 x 5 的数格，数格中已经给出了一些数，请你将剩下的空格填
写完整，使每行每列中都含有 1、2、3、4、5 这 5 个数字。
The following table is a 5x5 number grid. Some numbers have been given in the
number grid. Please fill in the remaining blanks so that each row and column
contains the 5 numbers 1, 2, 3, 4 and 5.

15. 把 1 到 12 分别填入六角形图案的 12 个圈圈中，使每条线上的四个数之和都
相等。AxB+CxD 的值为多少？
Fill in the blanks with 12 numbers from 1 to 12, so that the sum of the four
number on each line is equal. What is the value of AxB+CxD?

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庄老师 018-3801692 奥林匹克数学 Math Olympiad

16. 下表是一个 6 x 6 的数格，请你将下表填写完整，使每行、每列都含有 1、
2、3、4、5、6 这 6 个数字。
The following table is a 4x4 number grid. Please fill in the following table so that
each row and column contains the 6 numbers 1, 2, 3, 4, 5 and 6.

17. 把 A，B，C，D 填入六角形的圆圈内，使每条线上的 4 个圆圈都有 A，B，C
和 D。
Fill in the hexagonal circle with A, B, C and D so that each lie will have A, B, C and
D.

18. 内部四个交点上已填好数，在四周方格里填上适当的数，使交点上的数字恰
好等于四周四个方格内的和，应怎样填？
The four intersections have been filled in with numbers. Fill in the appropriate
number in the surrounding squares so that the numbers on the intersection are
exactly equal to the sum of the four surrounding squares. How to fill in?

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