Math puzzles, math puzzle questions

Elementary school, junior high school or high school, maybe you can take a look at the reference book for the civil service exam.

There are two identical candles, each of which burns out for 1 hour, how to make an accurate 45 minutes?

Answer: Light both ends of candle A and one end of candle B at the same time, and light the other end of candle B immediately when candle A burns out, and the time that passes when candle B burns out is 45 minutes.

Method 1:

There is no problem with 20 bottles at the beginning, and the next 10 bottles and 5 bottles are no problem, and then divide the 5 bottles into 4 bottles and 1 bottle, the first 4 empty bottles are replaced by 2 bottles, and the 2 bottles are replaced by 1 bottle after drinking, and the number of empty bottles left on hand after drinking is 2, and the 2 bottles are replaced by 1 bottle of soda, and the bottle exchanged for is returned to the bottle after drinking, so the maximum number of soda that can be drunk is: 20 10 5 2 1 1 1 40

Method 2: First look at how many bottles of soda you can drink for 1 yuan. Drink 1 bottle and 1 empty bottle, borrow 1 empty bottle from the merchant, replace 2 bottles with 1 bottle and continue to drink, and return the 1 empty bottle to the merchant after drinking. That is, 1 yuan can drink up to 2 bottles of soda. Of course, you can drink up to 40 bottles of soda for 20 yuan.

Method 3: Replace two empty bottles with one bottle of soda, you can know that pure soda is only worth 5 dimes. Of course, 20 yuan can drink up to 40 bottles of pure soda. Of course, you can drink up to 2n bottles of soda for n yuan.

Answer: 40 bottles.

20 yuan to buy 20 bottles of gas water; There are 20 empty bottles, and every two empty bottles are exchanged for one bottle of soda, which is exchanged for 10 bottles; 10 bottles for 5 bottles; 5 bottles for 2 bottles; The last 2 bottles are exchanged for 1 bottle; So add up to 20 + 10 + 5 + 2 + 1 = 38 bottles; Because the probability of another bottle in the soda activity is 25% (as one bottle for every four bottles is a winner), 38 divided by 4 to get 9 and 2, so 38 + 9 = 47 bottles;

For the first time, you can buy 20 bottles, and you can win 5 bottles and 10 bottles of soda, a total of 35 bottles, and the remaining 15 bottles;

The second time you use 15 bottles + borrow 1 bottle = 16 bottles can be exchanged for 8 bottles of soda, you can win 2 bottles, a total of 10 bottles of soda, and the remaining 10 bottles;

The third time, if you don't return the bottle, you will change it to 5 bottles of soda, and you will win 1 bottle, a total of 6 bottles of soda, and the remaining 6 bottles.

The fourth time I didn't return the bottle, 6 empty bottles were replaced with 3 bottles of soda, and the remaining 3 bottles were replaced;

The fifth time you don't return the bottle, borrow 1 more bottle, you can exchange it for 2 sodas;

Finally, after drinking the soda, the empty bottle is returned to the boss, and the transaction is closed.

A total of 35 + 10 + 6 + 3 + 2 = 56 bottles of soda can be drunk.

You can buy 20 bottles for the first time, and the probability of winning is 5 bottles, for a total of 25 bottles;

The second time, 25 bottles were exchanged for 12 bottles of water, and there was one empty bottle left, and the probability of winning the prize for 12 bottles was 3 bottles, with a total of 15 bottles and 1 empty bottle;

For the third time, 16 empty bottles are exchanged for 8 bottles, and the probability of winning is 2 bottles, for a total of 10 bottles;

The fourth time 10 empty bottles were exchanged for 5 bottles, and the probability of winning was 1 bottle, a total of 6 bottles;

The fifth time with 6 empty bottles in exchange for 3 bottles, the probability of winning the lottery is less than 1 bottle, so it can be ignored, a total of 3 bottles;

The sixth time, 2 of the 3 bottles in the fifth time were exchanged for 1 bottle of water, and 1 bottle was empty;

The seventh time is exchanged for 1 bottle with 2 bottles in the sixth round.

In summary, 25 + 15 + 10 + 6 + 3 + 1 + 1 = 61 bottles.

5020 2 (1 + 25 percent) = 50

It's a clever calculation. You can make equations if you don't understand them.

3 people + necklace = 23 1 formula person - 1 = 9 2 formula.

Necklace + glasses x necklace = 24 3 formulas.

Solution: 2 formulas:

Person = 10, substituting 1 formula to get:

30 + necklace = 23 get:

Necklace = -7 Substitute necklace = -7 into 3 formulas:

7+-7 glasses = 24 get:

7 (1 + glasses) = 24

1 + glasses = -24 7 (minus 24 out of 7).

Answer: 10+-7+-24 7=3+-24 7=-3 7 (minus 3/7).

3a+b=23

a+c-c/c=9 → a+c=10

b+cb=24 ->c+1=24/b

The last two lines get: a+24 b-1=10 a=11-24 b substituting the first line gets: 33-72 b+b=23 b2+10b-72=0 solve the quadratic equation to get:

b = 97-5 = (take a positive value) a + b + c = 10 + b = 97 + 5

a=11-24/b=11-24/(√97-5)=11-(√97+5)/3=(28-√97)/3=

c=24/b-1=24/(√97-5)-1=(√97+5)/3-1=(√97+2)/3=

Man 5 necklaces 8 glasses 2

1 trial person + (person necklace) + person 23

2 tries (man glasses) glasses glasses 9

3 try necklace glasses necklace 24

The symbol for 1 attempt is , and the symbol for 2 attempt is

（10*10-4）/4=24

There are only 8 lines planted into a square, and the landlord says 10 lines.

It should be planted like this.

( (Sunrise in the east and rain in the west.) , The Tao is sunny but affectionate

Let the defeat of Xiaohong speed grasp the trillion degree as the section dry rent a, the speed of the car is b, and the interval time is t;

10（a+b）=bt ①

15（b-a）=bt ②

Solution: b=5a; t=12