Distribute CookiesChef is making cookies for 𝑁N kids. He wants to give everyone an equal number of cookies. He must give at least 11 cookie to each kid.Chef already has 𝑀M cookies.He can destroy or make 11 cookie in 11 second.Find the minimum time after which he can evenly distribute the cookies between all kids.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of a single line of input.The first and only line of each test case contains 𝑁N and 𝑀M - the number of kids and the initial number of cookies.Output FormatFor each test case, output on a new line the minimum time such that Chef can evenly distribute all his cookies.Constraints1≤𝑇≤1041≤T≤10 4 1≤𝑁,𝑀≤1091≤N,M≤10 9 Sample 1:InputOutput45 175 184 12 182230Explanation:Test Case 1 : Chef destroys 22 cookies to have 1515 cookies total. This takes 22 seconds. Now, he can distribute all his cookies by giving every kid 33 cookies each.Test Case 2 : Chef makes 22 cookies to have 2020 cookies total. This takes 22 seconds again. Now, he can distribute all his cookies by giving every kid 44 cookies each.Test Case 3 : Chef makes 33 more cookies to have 44 cookies total, and he gives 11 each to the 44 kids. Note that Chef can't destroy 11 cookie and then evenly distribute, as he needs to give everyone at least 11 cookie.
Question
Distribute CookiesChef is making cookies for 𝑁N kids. He wants to give everyone an equal number of cookies. He must give at least 11 cookie to each kid.Chef already has 𝑀M cookies.He can destroy or make 11 cookie in 11 second.Find the minimum time after which he can evenly distribute the cookies between all kids.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of a single line of input.The first and only line of each test case contains 𝑁N and 𝑀M - the number of kids and the initial number of cookies.Output FormatFor each test case, output on a new line the minimum time such that Chef can evenly distribute all his cookies.Constraints1≤𝑇≤1041≤T≤10 4 1≤𝑁,𝑀≤1091≤N,M≤10 9 Sample 1:InputOutput45 175 184 12 182230Explanation:Test Case 1 : Chef destroys 22 cookies to have 1515 cookies total. This takes 22 seconds. Now, he can distribute all his cookies by giving every kid 33 cookies each.Test Case 2 : Chef makes 22 cookies to have 2020 cookies total. This takes 22 seconds again. Now, he can distribute all his cookies by giving every kid 44 cookies each.Test Case 3 : Chef makes 33 more cookies to have 44 cookies total, and he gives 11 each to the 44 kids. Note that Chef can't destroy 11 cookie and then evenly distribute, as he needs to give everyone at least 11 cookie.
Solution
The problem is asking to find the minimum time it will take for the Chef to evenly distribute cookies to all kids. The Chef can either make or destroy a cookie in one second. The Chef must give at least one cookie to each kid and wants to give an equal number of cookies to each kid.
Here are the steps to solve this problem:
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First, we need to find the remainder when the total number of cookies (M) is divided by the total number of kids (N). This will give us the number of extra cookies that cannot be evenly distributed.
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If the remainder is greater than half of the total number of kids, the Chef will need to make more cookies. The number of cookies to be made is the difference between the total number of kids and the remainder. This is because the Chef wants to give an equal number of cookies to each kid.
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If the remainder is less than or equal to half of the total number of kids, the Chef will need to destroy some cookies. The number of cookies to be destroyed is equal to the remainder.
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The minimum time required is equal to the number of cookies to be made or destroyed, as each operation takes one second.
This solution works because the Chef wants to give an equal number of cookies to each kid and each operation (making or destroying a cookie) takes one second. By finding the remainder when the total number of cookies is divided by the total number of kids, we can determine whether the Chef needs to make or destroy cookies and how many. The minimum time required is then equal to this number.
Similar Questions
Explanation:Test Case 1 : Chef destroys 22 cookies to have 1515 cookies total. This takes 22 seconds. Now, he can distribute all his cookies by giving every kid 33 cookies each.Test Case 2 : Chef makes 22 cookies to have 2020 cookies total. This takes 22 seconds again. Now, he can distribute all his cookies by giving every kid 44 cookies each.Test Case 3 : Chef makes 33 more cookies to have 44 cookies total, and he gives 11 each to the 44 kids. Note that Chef can't destroy 11 cookie and then evenly distribute, as he needs to give everyone at least 11 cookie.
Gia has 6 identical cookies. Starting today, she plans to eat at least 1 cookie each day until none are left. If the number of cookies she eats each day has to be a whole number, how many different ways can Gia distribute her cookies across the days?
Candy DistributionChef has 𝑁N candies. He has to distribute them to exactly 𝑀M of his friends such that each friend gets equal number of candies and each friend gets even number of candies. Determine whether it is possible to do so.NOTE: Chef will not take any candies himself and will distribute all the candies.Input FormatFirst line will contain 𝑇T, number of test cases. Then the test cases follow.Each test case contains of a single line of input, two integers 𝑁N and 𝑀M, the number of candies and the number of friends.Output FormatFor each test case, the output will consist of a single line containing Yes if Chef can distribute the candies as per the conditions and No otherwise.You may print each character of the string in uppercase or lowercase (for example, the strings yes, Yes, yEs, and YES will all be treated as identical).
Chef and Instant NoodlesChef has invented 11-minute Instant Noodles. As the name suggests, each packet takes exactly 11 minute to cook.Chef's restaurant has 𝑋X stoves and only 11 packet can be cooked in a single stove at any minute.How many customers can Chef serve in 𝑌Y minutes if each customer orders exactly 11 packet of noodles?Input FormatThe first and only line of input contains two space-separated integers 𝑋X and 𝑌Y — the number of stoves and the number of minutes, respectively.Output FormatPrint a single integer, the maximum number of customers Chef can serve in 𝑌Y minutesConstraints1≤𝑋,𝑌≤10001≤X,Y≤1000Sample 1:InputOutput3 721Explanation:Chef cooks for 𝑌=7Y=7 minutes and can cook 𝑋=3X=3 packets per minute, one on each stove.So, the total number of packets that can be cooked is 𝑋⋅𝑌=3⋅7=21X⋅Y=3⋅7=21.Each person orders one packet, so the maximum number of customers that can be served is 2121.
Anna has 20 plain cookies and 28 chocolate cookies. She is packing them into several boxes of the same size. She wants each box to have the same ratio between the two cookie types.What is the greatest number of boxes of cookies that she can she pack?
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