Math topic中文

Systematic enumeration

List all cases in a fixed order without repetition or omission, classifying first when needed.

Practice questions

  1. 1There are 81 grid points ( uniformly spaced ) in the square shown in the diagram below, including the points on the edge…
  2. 2When three positive integers aa, bb, and cc are multiplied together, their product is 100. Suppose a<b<ca < b < c. In ho…
  3. 3三年级（2）班有56名学生，这个月进行了两次数学测试：第一次得100分的学生的学号是6，9，15，16，27，33，56；第二次得100分的学生的学号是：7，9，16，27，36，40，48，51，53。 1．第一次得100分的有( )人。…
  4. 4Alina writes the numbers 1,2,…,91, 2, \dots, 9 on separate cards, one number per card. She wishes to divide the cards into 33…
  5. 5Buzz Bunny is hopping up and down a set of stairs, one step at a time. In how many ways can Buzz start on the ground, ma…
  6. 6A tetromino consists of four squares connected along their edges. There are five possible tetromino shapes, I, O, L, T,…
  7. 73个三位数乘积的算式 abc×bca×cab=234235286，（其中a＞b＞c）在校对时，发现右边的积的数字顺序出现错误，但是知道最后一位6是正确的．问：原式中的abc是多少？
  8. 8In an equiangular hexagon, all interior angles measure 120∘120^\circ. An example of such a hexagon with side lengths of 2,…
  9. 9Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then B…
  10. 10A △\triangle or ◯\bigcirc is placed in each of the nine squares in a 33-by-33 grid. Shown below is a sample configur…
  11. 11Akash's birthday cake is in the form of a 4×4×44 \times 4 \times 4 inch cube. The cake has icing on the top and the four si…
  12. 12用一副三角尺可以直接得到或可以拼出的锐角的个数总共有___个．
  13. 13A box contains five cards, numbered 11, 22, 33, 44, and 55. Three cards are selected randomly without replacement f…
  14. 14Any three vertices of the cube PQRSTUVWPQRSTUVW, shown in the figure below, can be connected to form a triangle. (For example,…
  15. 15Aaliyah rolls two standard 66-sided dice. She notices that the product of the two numbers rolled is a multiple of 66.…
  16. 16How many subsets of two elements can be removed from the set {1,2,3,4,5,6,7,8,9,10,11}\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\} so that the mean (a…
  17. 17In a sign pyramid a cell gets a "+" if the two cells below it have the same sign, and it gets a "-" if the two cells bel…
  18. 18On Monday Taye has 2.Everyday,heeithergains2. Every day, he either gains 3 or doubles the amount of money he had on the previous day. How many…