How many diagonals does a regular 20-sided polygon have?
Solution: By combination calculation, choose 2 from 20 = 190 and subtract 20 sides, 190-20 = 170.
2. The most frequent number of Mondays in 45 consecutive days is ()
How many Mondays are there for 45 consecutive days?
Answer: Think of the first day as Monday, 45- 1=44, 6×7=42, and it will appear six times, 6+ 1=7.
There are seven Mondays at most.
3. You have three weights: 1 kg, 3 kg, 9 kg and an equal arm balance, as shown in the figure.
How many different weights can you weigh with these three things?
As shown in the figure, you have three weights of 1 kg, 3 kg and 9 kg, and a balance with two arms of equal length.
How many kinds of objects with different weights can be weighed at most with these three weights?
Solution: Because I don't know my figure, I can only answer according to the general routine.
Combination: one out of three = 3, two out of three = 3, three out of three = 1, 3+3+ 1=7, 7 kinds.
There are no duplicate figures in these seven results, and there are at most seven.
4. The smallest natural number whose sum of digits is equal to 100 is ().
The sum of all the numbers is equal to 100. What is the smallest natural number?
Answer: To find the smallest natural number, the first consideration is that the number of digits must be at least.
To have the least number of digits, the bigger the number on each digit, the better.
100 ÷ 9 =11.11... at most 1 1 9,1.
Therefore, the minimum natural number satisfying the condition is199,999,999,999,999,999.
That is199.9 billion 99.99 million 9999.