A and B play a card game by taking 5 cards from a sufficient number of cards

k is a constant, 0 k 4 k = (1 .2 .3) A took 4 or (4-k) cards each time, a total of 15 times.

A's minimum number of cards is 15 * (4-3) = 15

The maximum number of cards to be taken is 15 * 4 = 60

B took 6 or (6-k) cards at a time, a total of 17 times, at least and at least took at least.

The minimum number of cards is 16 * (6-3) + 6 = 54

The maximum number of cards is 16 * 6 + 6 = 102

In the end, the total number of cards they took was exactly equal.

So the minimum number of cards is 54.

As can be seen from the title, the maximum range of the constant 0 A should be 15 * 4 = 60 cards, and the minimum should be 15 * (4-3) = 15 cards.

B's maximum range should be 17 * 6 = 102, and the minimum should be 6 + 16 * (6-3) = 54 cards.

B's 54 belongs to A's 15-60, so the minimum number of cards for two people should be 54 each, and the total is 54 + 54 = 108

In this case, assuming that A's card taking is x times to take 4 cards, then the case of taking 1 card is 15-x, so the specific situation of A is:

4*x+(15-x)*(4-3)=54, that is, 4x+15-x=54, 15+3x=54

It is obtained that x=13, that is, A takes 4 cards 13 times, and 1 card 2 times, which is equal to 54 cards.

And B takes 3 cards 16 times and 6 cards 1 time, which is equal to 54 cards.

54 playing cards, A and B take turns to take cards, each person can only take 1-4 cards each time, who gets the last card who loses, ask the first to take the card A how to ensure that it wins.

Take 4 first, the remaining 50 is a multiple of 5, the other party takes 1 you take 4, the other party takes 2 you take 3, bend pin one plus four equals 5, two plus macro pure three equals 5, so that a group of 5, the last 5 left, you take 4 more, the other party takes the last one, you win.

There are 54 playing cards, A and B take turns to take cards, each person can only take at least one at a time, up to five cards, how to get cards to ensure that A wins?

To ensure that A wins, A must first take a card. Solution: This problem is solved using the properties of remainders.

If A takes it first, because 54 (4+1), quotient 10 more than 4, so A takes Zhenming 4 first, B takes n (1 n 4) first, and then A takes (5-n) ; After each subsequent card in B, the number of cards taken by A is 5 minus the difference between the number of Sakura volts taken by the card of B's royal ode; In the end, there must be 54-49 = 5 pieces left, and B will take it, and B will have to give A 1 4 pieces no matter how he takes it. As a result, Ace will be able to take all the remaining cards at the end.

(1) Let A and B take the minimum number of cards respectively m, n then m = 15 (4 a k); n=6+16 (6-k), then m and n are both subtraction functions with respect to k.

2) because k is constant, and 0 (3) and the total number of cards taken by the two people in the end is exactly equal, then n takes the minimum value of 54, A can take 4 cards or (4-3) = 1 at a time, then A takes 15 times to make its number of cards 54

4) Then there is a minimum of 54 2 = 108 (cards).

The first solution.

If A takes (4-k) and B B takes (6-k), then A (15-a) takes 4 and B (17-b) takes 6, then A takes (60-ka) and B takes (102-kb).

Then the total number of cards: n = a (4-k) + 4 (15-a) + b (6-k) + 6 (17-b) = -k (a + b) + 162, so that to make the least number of cards, then n can be the smallest, because k is a positive number, the function is a subtraction function, then you can make (a + b) as large as possible, by the title, a 15, b 16, and finally the total number of cards taken by the two is exactly equal, so k (b-a) = 42, and 0 k 4, b-a is an integer, then by the knowledge of the divisible, k can be 1, 2,3, when k=1, b-a=42, because a 15, b 16, so this situation is rounded;

When k=2, b-a=21, because a 15, b 16, so this situation is rounded;

When k=3, b-a=14, then it can be in line with the topic, and it can be concluded that to ensure that a 15, b 16, b-a = 14, (a + b) value is maximum, then b = 16, a = 2;b=15，a=1；b=14，a=0；

When b = 16 and a = 2, a + b is the largest, a + b = 18, and then k = 3 and (a + b) = 18, so n = -3 18 + 162 = 108 sheets

So the answer is: 108

Set A takes x 4 cards, and B takes y times 6 cards (y 1,0 k 4).

According to the meaning of the title, it can be seen that the total number of cards taken by the two people is equal, so the equation can be listed 4x+(4-k)(15-k)=6y+(6-k)(17-y).

By simplification, k(2+x-y)=42

According to the title, k = 1, 2, 3

1) k=1,2+k-y=42, but x 15, y 16, rounded;

2) k=2,2+x-y=21, but x 15, y 16, rounded;

3）k=3,2+x-y=14,x=15，y=3；x=14，y=2；x=13，y=1；

x=15, y=3 15 4=60 (cards) 60 2=120 (cards) [because the total number of cards taken by the two is equal].

x=14,y=2 14 4+(15-14) (4-3)=57 (sheets) 57 2=114 (sheets) [Reason is the same as above].

x=13,y=1 13 4+(15-13) (4-3)=54 (sheets) 54 2=108 (sheets) [Reason is the same as above].

So there are at least 108 cards.

If there is anything wrong in the answering process, please understand, I am only the first year of junior high school =. = Thank you

Solution: Let A take (4-k) times, B B times take (6-k) cards, then A (15-a) times take 4 cards, B (17-b) times take 6 cards, then A takes cards (60-ka), B takes cards (102-kb) cards then a total of cards: n = a (4-k) + 4 (15-a) + b (6-k) + 6 (17-b) = -k (a + b) + 162, so that to make the least cards, then n can be the smallest, because k is a positive number, the function is a subtraction function, then you can make (a +b) as large as possible, from the title, a 15, b 16, and finally the total number of cards taken by the two is exactly equal, so k(b-a) = 42, and 0 k 4, b-a is an integer, then by the knowledge of the divisible, k can be 1,2,3, when k = 1, b-a = 42, because a 15, b 16, so this situation is rounded; When k=2, b-a=21, because a 15, b 16, so this situation is rounded; When k=3 and b-a=14, it can meet the meaning of the topic

To ensure that the values of a 15, b 16, b-a=14, (a+b) are maximized, then b = 16, a = 2;b=15，a=1；b=14，a=0；When b = 16, a = 2, a + b is the maximum, a + b = 18, and then k = 3, (a + b) = 18, so n = -3 18 + 162 = 108 So the answer is: 108 Solution: Let A take (4-k) and B b take (6-k), then A (15-a) takes 4 cards, B (17-b) takes 6 cards, then A takes cards (60-ka), B takes cards (102-kb) and then takes a total of cards:

n = a (4-k) + 4 (15-a) + b (6-k) + 6 (17-b) = -k (a + b) + 162, so that to make the least number of cards, then n can be the smallest, because k is a positive number, the function is a subtraction function, then (a + b) can be as large as possible, from the title, a 15, b 16, and finally the total number of cards taken by the two is exactly equal, so k(b-a) = 42, and 0 k 4, b-a is an integer, then by the knowledge of divisible, k can be 1, 2, 3, when k =1, b-a=42, because a 15, b 16, so this situation is rounded; When k=2, b-a=21, because a 15, b 16, so this situation is rounded; When k=3, b-a=14, then it can be in line with the topic, and it can be concluded that to ensure that a 15, b 16, b-a = 14, (a + b) value is maximum, then b = 16, a = 2;b=15，a=1；b=14，a=0；When b = 16 and a = 2, a + b is the maximum, a + b = 18, and then k = 3, (a + b) = 18, so n = -3 18 + 162 = 108 sheets So the answer is: 108

A and B play card games, A takes 4 cards or (4-k) cards each time, B takes 6 cards or (6-k) cards each time, A takes 15 times, B takes 17 times and two people on one side more than 17 times, and asks how many cards there are at least.

Is it the second year of junior high school? Hehe, I also want to ask which ......

1. A 5 and then B 3 and finally C 2, after a round, they get a total of 10 cards.

Cards are dealt exactly 5 rounds.

3. In the end, the crack is just right, and C sells the 50th card early.

The fundamental reason for many love cups is: too early to enter the play.

You will always be the amber in my heart, and I may be just a little sand in your way.

Every failure is a foreshadowing of success; For every test, there is a gain; Every time there is a tear, there is an awakening; With every tribulation, there is the wealth of life. Every pain is a pillar of growth. Every blow is a strong backing; There are some setbacks to be alive, and we are still strong to overcome every setback, and as long as we are alive, we are worth thanking.