The problem is asking to find the maximum product of three numbers (a, b, c) after increasing any of these numbers up to 5 times by 1. Here are the steps to solve this problem: 1. First, we need to sort the numbers a, b, and c in ascending order. This is because we want to increase the smallest numbers first to get the maximum product. 2. Then, we increase the smallest number by 1, up to 5 times. If we have increased a number 5 times and there are still increments left, we move to the next smallest number. 3. After we have made all the increments, we calculate the product of the three numbers. 4. We repeat these steps for each test case. Here is a Python solution for the problem: ```python t = int(input()) for _ in range(t): a, b, c = sorted(map(int, input().split())) for _ in range(5): if a < b: a += 1 else: b += 1 print(a * b * c) ``` This solution works by first reading the number of test cases. For each test case, it reads the three numbers and sorts them. Then it increases the smallest number by 1, up to 5 times. If the smallest number becomes larger than the next smallest number during this process, it starts to increase the next smallest number. Finally, it prints the product of the three numbers.

A. Only Plusestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputKmes has written three integers a𝑎, b𝑏 and c𝑐 in order to remember that he has to give Noobish_Monk a×b×c𝑎×𝑏×𝑐 bananas.Noobish_Monk has found these integers and decided to do the following at most 55 times:pick one of these integers;increase it by 11.For example, if a=2𝑎=2, b=3𝑏=3 and c=4𝑐=4, then one can increase a𝑎 three times by one and increase b𝑏 two times. After that a=5𝑎=5, b=5𝑏=5, c=4𝑐=4. Then the total number of bananas will be 5×5×4=1005×5×4=100.What is the maximum value of a×b×c𝑎×𝑏×𝑐 Noobish_Monk can achieve with these operations?InputEach test contains multiple test cases. The first line of input contains a single integer t𝑡 (1≤t≤10001≤𝑡≤1000) — the number of test cases. The description of the test cases follows.The first and only line of each test case contains three integers a𝑎, b𝑏 and c𝑐 (1≤a,b,c≤101≤𝑎,𝑏,𝑐≤10) — Kmes's integers.OutputFor each test case, output a single integer — the maximum amount of bananas Noobish_Monk can get.ExampleinputCopy22 3 410 1 10outputCopy100600

Question

A. Only Plusestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputKmes has written three integers a𝑎, b𝑏 and c𝑐 in order to remember that he has to give Noobish_Monk a×b×c𝑎×𝑏×𝑐 bananas.Noobish_Monk has found these integers and decided to do the following at most 55 times:pick one of these integers;increase it by 11.For example, if a=2𝑎=2, b=3𝑏=3 and c=4𝑐=4, then one can increase a𝑎 three times by one and increase b𝑏 two times. After that a=5𝑎=5, b=5𝑏=5, c=4𝑐=4. Then the total number of bananas will be 5×5×4=1005×5×4=100.What is the maximum value of a×b×c𝑎×𝑏×𝑐 Noobish_Monk can achieve with these operations?InputEach test contains multiple test cases. The first line of input contains a single integer t𝑡 (1≤t≤10001≤𝑡≤1000) — the number of test cases. The description of the test cases follows.The first and only line of each test case contains three integers a𝑎, b𝑏 and c𝑐 (1≤a,b,c≤101≤𝑎,𝑏,𝑐≤10) — Kmes's integers.OutputFor each test case, output a single integer — the maximum amount of bananas Noobish_Monk can get.ExampleinputCopy22 3 410 1 10outputCopy100600

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Solution 1

The problem is asking to find the maximum product of three numbers (a, b, c) after increasing any of these numbers up to 5 times by 1.

Here are the steps to solve this problem:

First, we need to sort the numbers a, b, and c in ascending order. This is because we want to increase the smallest numbers first to get the maximum product.
Then, we increase the smallest number by 1, up to 5 times. If we have increased a number 5 times and there are still increments left, we move to the next smallest number.
After we have made all the increments, we calculate the product of the three numbers.
We repeat these steps for each test case.

Here is a Python solution for the problem:

t = int(input())
for _ in range(t):
    a, b, c = sorted(map(int, input().split()))
    for _ in range(5):
        if a < b:
            a += 1
        else:
            b += 1
    print(a * b * c)

This solution works by first reading the number of test cases. For each test case, it reads the three numbers and sorts them. Then it increases the smallest number by 1, up to 5 times. If the smallest number becomes larger than the next smallest number during this process, it starts to increase the next smallest number. Finally, it prints the product of the three numbers.

This problem has been solved

Solution 2

The problem is asking for the maximum product of three numbers (a, b, c) after increasing any of these numbers by 1 up to 5 times.

Here are the steps to solve this problem:

Read the number of test cases, t.
For each test case, read the three numbers a, b, c.
Sort the numbers a, b, c in ascending order. This is because we want to increase the smallest numbers first to get the maximum product.
While we still have increases left (up to 5) and we have not yet increased the largest number twice, increase the smallest number. If the smallest number becomes larger than the second smallest number, update their positions. Decrease the number of remaining increases.
If we still have increases left, distribute them equally between the two largest numbers. If there is one increase left, assign it to the smaller of the two numbers.
The maximum product is now abc. Print this number.
Repeat steps 2-6 for each test case.

This algorithm ensures that we always increase the smallest numbers first, which will lead to the maximum possible product.

This problem has been solved

Similar Questions

Kmes has written three integers a𝑎, b𝑏 and c𝑐 in order to remember that he has to give Noobish_Monk a×b×c𝑎×𝑏×𝑐 bananas.Noobish_Monk has found these integers and decided to do the following at most 55 times:pick one of these integers;increase it by 11.For example, if a=2𝑎=2, b=3𝑏=3 and c=4𝑐=4, then one can increase a𝑎 three times by one and increase b𝑏 two times. After that a=5𝑎=5, b=5𝑏=5, c=4𝑐=4. Then the total number of bananas will be 5×5×4=1005×5×4=100.What is the maximum value of a×b×c𝑎×𝑏×𝑐 Noobish_Monk can achieve with these operations?InputEach test contains multiple test cases. The first line of input contains a single integer t𝑡 (1≤t≤10001≤𝑡≤1000) — the number of test cases. The description of the test cases follows.The first and only line of each test case contains three integers a𝑎, b𝑏 and c𝑐 (1≤a,b,c≤101≤𝑎,𝑏,𝑐≤10) — Kmes's integers.OutputFor each test case, output a single integer — the maximum amount of bananas Noobish_Monk can get.ExampleinputCopy22 3 410 1 10outputCopy100600

Chef is eagerly waiting for a piece of information. His secret agent told him that this information would be revealed to him after 𝐾K weeks.𝑋X days have already passed and Chef is getting restless now. Find the number of remaining days Chef has to wait for, to get the information.It is guaranteed that the information has not been revealed to the Chef yet.Input FormatThe first line of input will contain an integer 𝑇T — the number of test cases. The description of 𝑇T test cases follows.The first and only line of each test case contains two space-separated integers 𝐾K and 𝑋X, as described in the problem statement.Output FormatFor each test case, output the number of remaining days that Chef will have to wait for.Constraints1≤𝑇≤5001≤T≤5001≤𝐾≤101≤K≤101≤𝑋<7⋅𝐾1≤X<7⋅KSample 1:InputOutput41 51 61 11 22165Explanation:Test case 11: The information will be revealed to the Chef after 11 week, which is equivalent to 77 days. Chef has already waited for 55 days, so he needs to wait for 22 more days in order to get the information.Test case 22: The information will be revealed to the Chef after 11 week, which is equivalent to 77 days. Chef has already waited for 66 days, so he needs to wait for 11 more day in order to get the information.Test case 33: The information will be revealed to the Chef after 11 week, which is equivalent to 77 days. Chef has already waited for 11 day, so he needs to wait for 66 more days in order to get the information.Test case 44: The information will be revealed to the Chef after 11 week, which is equivalent to 77 days. Chef has already waited for 22 days, so he needs to wait for 55 more days in order to get the information.

A monkey is climbing a tree. For the first second and all the consecutive odd seconds, the monkey goes up by a𝑎 meters and for every consecutive even second after the first, the monkey comes down by b𝑏 meters.Find the height the monkey reaches after n𝑛 seconds.InputThe first line has two integers a𝑎 and b𝑏 (0≤b≤a≤0≤𝑏≤𝑎≤ 104104)The second line has a single integer n𝑛 (00 ≤n≤≤𝑛≤ 105105)OutputPrint a single integer, the height reached by the monkey after n𝑛 secondsExampleinputCopy5 34outputCopy4NoteThe monkey moves 55 meters up in the 1st1𝑠𝑡 and 3rd3𝑟𝑑 second and 33 meters down in the 2nd2𝑛𝑑 and 4th4𝑡ℎ second, thus the monkey reaches 5+5−3−3=45+5−3−3=4 meters after 44 seconds.

D. World is Minetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAlice and Bob are playing a game. Initially, there are n𝑛 cakes, with the i𝑖-th cake having a tastiness value of ai𝑎𝑖.Alice and Bob take turns eating them, with Alice starting first:In her turn, Alice chooses and eats any remaining cake whose tastiness is strictly greater than the maximum tastiness of any of the cakes she's eaten before that. Note that on the first turn, she can choose any cake.In his turn, Bob chooses any remaining cake and eats it.The game ends when the current player can't eat a suitable cake. Let x𝑥 be the number of cakes that Alice ate. Then, Alice wants to maximize x𝑥, while Bob wants to minimize x𝑥.Find out how many cakes Alice will eat if both players play optimally.InputEach test contains multiple test cases. The first line of input contains a single integer t𝑡 (1≤t≤5001≤𝑡≤500) — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer n𝑛 (1≤n≤50001≤𝑛≤5000) — the number of cakes.The second line of each test case contains n𝑛 integers a1,a2,…,an𝑎1,𝑎2,…,𝑎𝑛 (1≤ai≤n1≤𝑎𝑖≤𝑛) — the tastiness values of the cakes.It is guaranteed that the sum of n𝑛 over all test cases does not exceed 50005000.OutputFor each test case, output a single integer — the number of cakes Alice will eat if both players play optimally.ExampleinputCopy941 4 2 331 1 151 4 2 3 443 4 1 41184 3 2 5 6 8 3 476 1 1 3 5 3 1116 11 6 8 7 5 3 11 2 3 5172 6 5 3 9 1 6 2 5 6 3 2 3 9 6 1 6outputCopy213213244NoteIn the first test case, one possible sequence of turns is:Alice eats a cake with a tastiness value of 11. The remaining cakes are [4,2,3][4,2,3].Bob eats a cake with a tastiness value of 22. The remaining cakes are [4,3][4,3].Alice eats a cake with a tastiness of 33. The remaining cakes are [4][4].Bob eats a cake with a tastiness value of 44. The remaining cakes are [][].Since there are no more cakes left, the game ends.In the second test case, one possible sequence of turns is:Alice eats a cake with a tastiness value of 11. The remaining cakes are [1,1][1,1].Bob eats a cake with a tastiness value of 11. The remaining cakes are [1][1].Since Alice has already eaten a cake with a tastiness value of 11, she cannot make a turn, so the game ends.

Long DriveChef and Chefina are out on a long road trip.The average speed of the car after 1010 hours of driving is 𝑋X kilometres per hour.Chef wants to achieve an average speed of 𝑌Y kilometres per hour. Given that he can travel a maximum of 100100 kilometres in one hour, find the minimum number of additional integer hours required for him to reach the target average speed.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of two space-separated integers 𝑋X and 𝑌Y — the average speed after 1010 hours of driving and the required average speed.Output FormatFor each test case, output on a new line, the minimum number of integer hours required for him to reach the target average speed.Constraints1≤𝑇≤12251≤T≤122550≤𝑋<𝑌<10050≤X<Y<100Sample 1:InputOutput350 5160 8055 9511080Explanation:Test case 11: The average speed after 1010 hours is 5050 kmph. This means that Chef has travelled a distance of 50⋅10=50050⋅10=500 kilometres. If he covers 6161 kilometres in the next hour, his average speed would be (500+61)(10+1)=51(10+1)(500+61) =51. Thus, he can achieve the target average speed in one hour.Test case 22: The average speed after 1010 hours is 6060 kmph. This means that Chef has travelled a distance of 60⋅10=60060⋅10=600 kilometres. If he covers 100100 kilometres each for the next 1010 hours, his average speed would be (600+100⋅10)(10+10)=80(10+10)(600+100⋅10) =80. Thus, he can achieve the target average speed in minimum of 1010 hours.

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