Take a nest of eggs, one more than half at a time. Take it 4 times

There are x pcs. First time left: x-x 2-1 Simplified to: x 2-1 Second time left: x 2-1-(x 2-1) 2-1 Reduced to: x 4-3 2

The third time left: x 4-3 2-(x 4-3 2) 2-1 Reduced to: x 8-7 4

The fourth time left: x 8-7 4-(x 8-7 4) 2-1=0 solution: x=30

There are 30 in total, 16 for the first time, 8 for the second time, 4 for the third time, and 2 for the fourth time.

According to the regression method, it can be seen that the last time there were 2, before the last time there were (2+1)*2=6, before the penultimate there were (6+1)*2=14, before the second time there were (14+1)*2=30, before the first time there were (30+1)*2=62.

Let's say there are x eggs in total.

First time left: x-x 2-1 Simplified to: x 2-1 Second time left: x 2-1-(x 2-1) 2-1 Reduced to: x 4-3 2

The third time left: x 4-3 2-(x 4-3 2) 2-1 Reduced to: x 8-7 4

The fourth time left: x 8-7 4-(x 8-7 4) 2-1=0 solution: x=30

The analysis showed that there were up to 47 eggs in this box.

Specific analysis steps:

1. The first condition is less than 50 (less than must not be greater than or equal to). For example...And so on, these numbers are met.

2. The second condition must be a number that is divisible by 2 and has a remainder of 1 while satisfying the first condition. For example...And so on these numbers (singular numbers greater than 2) are satisfied.

3. On the basis that the third condition satisfies the first condition, it must be a number that can also be divisible by 3 and have a remainder of 2. For example...And so on, these numbers are met.

4. The fourth condition satisfies the above is the number that satisfies all the above conditions. For example...And so on, these numbers are met.

5. The last condition, all the above conditions are met and the number is the largest number, and the maximum number can be obtained through the fourth condition. So the answer is 47.

Two of the two numbers have one left, indicating that it is an odd number. 4 of the remaining 5 numbers means that the mantissa is 9 or 43 3 numbers are finished, which means that it is divisible by 3 and 49 is not good, so it is 39

Less than 50 proves less than 50, but closer to 50; Take 2 and leave 1 to prove that it is singular; Take 3 and leave 2 to prove that it is not a multiple of 3. Then try one by one, first 49, but 49 divided by 3, and the remainder is 1, so it is not 49; Then it's 47, and 47 divided by 3 remainder is that all the requirements are met, so it's 47.

Two of the two numbers have one left, indicating that it is an odd number.

If there are 4 remaining out of 5, it means that the mantissa is 9 or 4

3 3 numbers are counted, which means that they are divisible by 3.

49 doesn't work, so it's 39

Up to 47, analysis: take 2 and leave one, it must be a singular number, take 3 and leave 2, which is a multiple of 3 plus 2

There can be up to 47 of them.

Take two and leave 1 at a time, it must be an odd number.

Take 3 and leave two, the total is less than 50 and is singular, 49-2=47, 47 3 is not an integer.

And 47-2 = 45 and 45 3 = 15, so the answer is 47.

18 (pcs) A: There were 18 eggs in this box.

A carton of eggs, half of the first day was eaten and there was 1 more, and the second day I ate the remaining half and there was one more, and there were 3 eggs left at this time? Draw a picture to show it.

Take two at a time and leave one, and take three at a time and leave two means that if there is one more, then two collapses and two can be taken, and three or three can be taken. So the number of eggs is a common multiple of the width of 2 and 3 minus a lump of noisy land.

There is a minimum of 2*3-1=5.

The least common multiple of 2 and 3 is 6

The number of eggs is 1 less than the multiple of 2 and 3

So there are up to 6 8-1 = 47.

Take them one by one, just finished.

2 2 take, 1 left.

Take 3 of 3 and take it just over.

4 4 take, 1 left. '

5 5 take, 4 left.

6 6 take, 3 left.

Take 7 7 and take it just right.

8 8 take, 1 left.

Take 9 of 9 and take it just over.

Q: How many eggs are in the basket? Can anyone tell me the answer.

x(n)=1449+(n-1)*2520, n is a natural number, that is, an integer greater than or equal to 1.

This is a series of equal differences with countless answers, the minimum value is 1449, and the tolerance is 2520, (in fact, the least common multiple of 1 9 these 9 numbers is 2520, 5 * 7 * 8 * 9 = 2520, students who are good at mathematics can see that in the numbers less than 2520, only one number meets the conditions, and the single digit must be 9, and then it is a multiple of 63 * 3 = 189, 6 6 have a remainder, 9 9 have no remainder, indicating that it is an odd multiple, so the range is smaller)

So how to get the specific formula, this is a headache, you need to solve a system of multivariate equations, suppose there are m eggs, there is the following formula:

m=2a+1=3b=4c+1=5d+4=6e+3=7f=8g+1=9h, where a, b, c, d, e, f, g are all natural numbers, combined with the least common multiple of 2520, the solution of this system of equations will be obtained.

a=724+(n-1)*1260, b=483+(n-1)*840, c=362+(n-1)*630, d=289+(n-1)*504, e=241+(n-1)*420, f=207+(n-1)*360, g=181+(n-1)*315, h=161+(n-1)*161, so that the minimum value of x is calculated to be 1449. Combine it with tolerances and the complete formula:

x(n)=1449+(n-1)*2520

On further observation, this question is a bit verbose and can be further simplified into the following question:

A basket of eggs. 5 5 take, 4 left.

6 6 take, 3 left.

Take 7 7 and take it just right.

8 8 take, 1 left.

Take 9 of 9 and take it just over.

Q: How many eggs are in the basket?

Who's eggs are also taken one by one.

A basket of eggs: Take them one by one, just finished. 2 2 take, 1 left.

Take 3 of 3 and take it just over. 4 4 take, 1 left. 5 5 take, 1 left.

6 6 take, 3 left. Take 7 7 and take it just right. 8 8 take, 1 left.

Take 9 of 9 and take it just over. Q: How many eggs are at least in the basket?

Answers as well as analysis:

There are at least 441 eggs in the basket.

1. Take it one by one, just finished; Take 3 of 3 and take it just over. Take 7 7 and take it just right. Take 9 of 9 and take it just over. Explain that the number of eggs is a common multiple of 7 and 9, and then take 2 and 2, and there is 1 left, indicating that the number of eggs is a common multiple of 7 and 9 and is not an even number. The number of eggs that meet this condition may be 、...

2. According to 2 2 takes, there is 1 left; 4 4 take, 1 left. 5 5 take, 1 left. 8 8 take, 1 left. Indicates that the number of eggs is 1 more than the common multiple of 5 and 8. The number of eggs that meet this condition may be 、...

The minimum number that meets both of the above conditions is 441 because 441 6 = 73 ......3. Meet the conditions of 6 out of 6 and 3 left.

So, to sum up, there are at least 441 eggs in the basket.

A basket of eggs: Take them one by one, just finished.

2 2 take, 1 left.

Take 3 of 3 and take it just over.

4 4 take, 1 left.

5 5 take, 1 missing.

6 6 take, 3 left.

Take 7 7 and take it just right.

8 8 take, 1 left.

Take 9 of 9 and take it just over.

Q: How many eggs are at least in the basket?

Answer: There are at least 1449 eggs in the basket.

Analysis: 1. According to 5 5 takes, there is still 1 difference. It means that one more egg is a multiple of 5, so the single digit of the number of eggs is 4 or 9;

2. Take it one by one, just finished; Take 3 of 3 and take it just over. Take 7 7 and take it just right. Take 9 of 9 and take it just over. Explain that the number of eggs is a common multiple of 7 and 9, and the least common multiple of 7 and 9 is 63, so the number of eggs is a multiple of 63;

3. According to 2 2 takes, there is 1 left; 4 4 take, 1 left. 8 8 take, 1 left. The number of eggs is an odd number, and the last three digits of the difference between the number of eggs and 1 are multiples of 8.

Based on the three aspects of the appeal, it shows that the number of eggs is a multiple of 63, and the single digit is 9, so the number of eggs may be 33、......

It has been verified to be at least 63 23 = 1449, which meets the third condition above. Bring 1449 into "6 6 to take, 3 left." The conditions are also met.

So, there are at least 1,449 eggs in the basket.

Based on the 9 conditions given, 9 judgments can be drawn.

, i.e., any non-zero integer.

2. Not divisible by 2, it is an odd number, and the remainder of the number divided by 2 is a multiple of .

4. Not divisible by 4, not a multiple of 4, the remainder of the number divided by 4 is 15, not divisible by 5, not a multiple of 5, the remainder of the number divided by 5 is 16, not divisible by 6, not a multiple of 6, the remainder of the number divided by 6 is a multiple of .

8. Not divisible by 8, not a multiple of 8, the remainder of the number divided by 8 is a multiple of .

To sum up, using Excel's remainder formula and filtering function, the smallest number that meets the requirements is 441, which means that there are at least 441 eggs in the basket. In addition, within 12,000, there are still the number of eligible people