Sunday, July 26th

Today, when I was doing the Olympic math problem, I met a very confused problem. The problem is this: 37 students want to cross the river, and there is an empty boat at the ferry, which can only take five people. How many times must they cross the river with this boat?

Careless people often neglect punting, so they can only sit four people at a time. In this way, 37 people subtract one rowing classmate, leaving 36 students, 36 divided by 4 equals 9, and the classmate who worked as a boatman on the other side for the last time also landed 4, so it takes at least 9 trips.

This seemingly simple question is actually a mystery. Therefore, mathematics can't be sloppy!

Monday, July 27th

In the evening, I saw a problem in the Olympiad Book: the number of apple trees in the orchard is three times that of pear trees. Master Lao Wang fertilizes 50 apple trees and 20 pear trees every day. A few days later, all the pear trees were fertilized, but the remaining 80 apple trees were not fertilized. Excuse me: How many apple trees and pear trees are there in the orchard?

I am not intimidated by this question, but it can stimulate my interest. I think the apple tree is three times as big as the pear tree. If two kinds of trees are to be fertilized on the same day, Master Lao Wang will fertilize "20×3" apple trees and 20 pear trees every day. In fact, he only fertilizes 50 apple trees every day, which is 10, and the last 80 trees. Therefore, Master Lao Wang has been fertilizing for 8 days. 20 pear trees a day, 8 days is 160 pear trees. According to the first condition, there are 480 apple trees.

This is to solve the problem with the idea of hypothesis, so I think the hypothesis method is really a good way to solve the problem.

Tuesday, July 28th

Two days ago, when I was looking through my classmates' Olympic math books, I found such a problem. If the sum of a four-digit number and a three-digit number is 1999, and the four-digit number and the three-digit number are composed of seven different numbers. So, how many such four digits can there be at most?

I think I can't figure it out even if it is broken, so I have to look at the answer: in order to calculate the maximum number of such four digits, the conditions of A, B, C, D, E, F and G are different, so we can see that B (b≠ 1, 8,9) has seven ways to select numbers, and C(C≦) So according to the principle of multiplication, there can be at most four digits like (7×6×4=) 168.

Ah! Mathematics is really wonderful!

Wednesday, July 29th

Today, my father and I played a game: grab 30 newspapers. The rules of this game are simple: everyone can report at most three natural numbers at a time, and at least one natural number. When reporting natural numbers, you can't repeat them or skip them. Whoever gets to 30 first wins.

I played with my dad several times, sometimes I won, sometimes my dad won, and it was basically a draw. I thought to myself: how can I win every time I rob a newspaper? Is there a little rule hidden in this game? What is this rule? I told my mother my doubts. My mother said, "I'm watching you play games. I think if the sum of the numbers of the two of you in each round is 4, the first one will definitely win. " I thought about it and said, "Mom, what's the matter? I can't say it now. " Dad and I continue to play, let's find this rule! "Dad was tired and said," Let's play tomorrow! " "

To be continued …

Thursday, July 30th

I also noticed that as long as I grab the number 26 first every time, I will definitely win. Because if I grab the number 26 first, and there are still four numbers until the number 30, according to the rules of the game, one person can report at most three numbers and at least one number at a time, then when my father reports a number "27", I will report three numbers "28, 29, 30", and I will grab the number 30 first; Dad reported two numbers "27, 28" and I reported two numbers "29, 30", so I can grab 30 first; When dad reported three numbers "27, 28, 29", I reported a number "30" and won. It seems that getting the number 26 first is definitely a guarantee of victory. So, besides grabbing the number 26? In the previous round, what figures must I determine to ensure my victory? According to the method of grabbing the number 26 first, I made a calculation: to win, we must grab these numbers firmly in every round. They are 22, 18, 14, 10, 6 and 2 respectively. So, is this the rule of this game? I have to verify it in the game.

With this idea, I feel confident of victory, and sure enough, I am a shoo-in.

After learning my method, my father encouraged me to say, "It's good that you can figure it out yourself." I am happy again: "Dad, I will find a more interesting math game to play with you next time!" " "

Friday, July 365438 +0

Today I found another Olympic math problem: Xiao Ming read an English book. The first time I read it, I read 35 pages on the first day, and then I read 5 pages more every day than the day before. As a result, he only read 35 pages on the last day. The second time, I read 45 pages on the first day, and then I read 5 more pages every day than the day before. As a result, I only need to read 40 pages on the last day. How many pages are there in this book?

I thought for a while, and the answer came out: the first plan: 35, 40, 45, 50, 55, ... 35; Second plan: 45, 50, 55, 60, 65, ... 40; The second plan is adjusted as follows: the first plan: 40, 45, 50, 55, ...