Combinations that add up to 15

The Combinations Calculator will find the number of possible combinations that can be obtained by taking a sample of items from a larger set. Basically, it shows how many different possible subsets can be made from the larger set.

Combinations and Permutations Calculator

For this calculator, the order of the items chosen in the subset does not matter. Also referred to as r-combination or "n choose r" or the binomial coefficient. In some resources the notation uses k instead of r so you may see these referred to as k-combination or "n choose k. You have won first place in a contest and are allowed to choose 2 prizes from a table that has 6 prizes numbered 1 through 6. How many different combinations of 2 prizes could you possibly choose?

In this example, we are taking a subset of 2 prizes r from a larger set of 6 prizes n. A teacher is going to choose 3 students from her class to compete in the spelling bee.

Combinations Calculator (nCr)

She wants to figure out how many unique teams of 3 can be created from her class of In this example, we are taking a subset of 3 students r from a larger set of 25 students n. A restaurant asks some of its frequent customers to choose their favorite 4 items on the menu.

If the menu has 18 items to choose from, how many different answers could the customers give? Here we take a 4 item subset r from the larger 18 item menu n. First, let's find the total handshakes that are possible. That is to say, if each person shook hands once with every other person in the group, what is the total number of handshakes that occur? A way of considering this is that each person in the group will make a total of n-1 handshakes.

Since there are n people, there would be n times n-1 total handshakes. In other words, the total number of people multiplied by the number of handshakes that each can make will be the total handshakes. However, this includes each handshake twice 1 with 2, 2 with 1, 1 with 3, 3 with 1, 2 with 3 and 3 with 2 and since the orginal question wants to know how many different handshakes are possible we must divide by 2 to get the correct answer.

The order of the items chosen in the subset does not matter so for a group of 3 it will count 1 with 2, 1 with 3, and 2 with 3 but ignore 2 with 1, 3 with 1, and 3 with 2 because these last 3 are duplicates of the first 3 respectively. For more information on combinations and binomial coefficients please see Wolfram MathWorld: Combination. Basic Calculator. Discrete Math. Combinations Calculator nCr. Combinations nCr Calculator.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Puzzling Stack Exchange is a question and answer site for those who create, solve, and study puzzles. It only takes a minute to sign up. In a 3x3 grid, I'd have to put numbers from 1 to 9 in a manner so that respective row, column and diagonal add up to Is there any strategy or way of approach to this problem, or is trial and error method the solution to it?

As the square square is symmetric there are eight symmetries. You can also get these symmetries by a simple variation of the start square and direction used in step 2. The row above does not exist so move to the last row of the square in the same column. If you were in the last column you would move to the first column. If you look at the example of the 5x5 at number The next position is the square up and to the right of 15 which wraps on both the row and column to point to the lower right square which has 11 in it.

As that square is not empty we placed 16 underneath No others are solvable without guessing one but from there you just solve them one at a time. Finally the last two squares can be easily solved. Then it becomes 3x3 boxes. For the remaining boxes, put the number which is opposite to the box. Another approach is to consider the ways to obtain 15 as a sum of 3 different numbers in the range As you can see there are only 8 ways, and you need 8 different sums in your square.

So each sum appears exactly once as a line in your square. Only the center belongs to 4 lines. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.

Puzzle of putting numbers in 3x3 Grid to add up to 15 Ask Question. Asked 5 years, 8 months ago. Active 3 years, 5 months ago. Viewed k times. Freya Freya 99 1 1 gold badge 1 1 silver badge 3 3 bronze badges. Jul 30 '14 at How the heck did this get so many views? Did it make Hot Network Questions for a year?! Active Oldest Votes. If that square is empty enter the next number; if the square is not empty put the next number underneath the last number you entered. All rows, columns and the two diagonals will sum to the same value. Alan Alan 4 4 bronze badges. Does this method have a name? It helped me very much.

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It is a very nice way and I am glad to have been taught this.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information.

I am writing a program that deals with cards and a hand. A hand has 5 cards. I want to know whats a good algorithm for deciding which combination of cards add up to Kings, Queens, Jacks, count as 10 and a Ace count as one. This is very similar to subset sums, which I recently answered here: Subset Sum algorithm. Learn more. Looking for combinations that add up to 15 in a card of hands Ask Question. Asked 9 years, 4 months ago. Active 9 years, 4 months ago.

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Hottest Questions. Previously Viewed. Unanswered Questions. Math and Arithmetic. Wiki User If the 6 digits can be repeated, there are different combinations. If you cannot repeat digits in the combination there are different combinations. If you have 6 different digits, you can make only 15 4-digit combinations from them. Asked in Math and Arithmetic, Statistics How may 4 digit number parlay combinations are possible by using 6 numbers And what are the combinations?

There are 15, and they are Asked in Math and Arithmetic, Algebra What are all of the possible numeric combinations using starting with 15? As the number has to start with 15, we have only 3 remaining digits to work with. There are 3 possible options for the first digit. Then out of each of these, 2 possible options for the second digit, and one option for the last. This means that in total there are 3x2x1 6 possible combinations. These are: There are infinite combinations that can make Asked in Math and Arithmetic What times what equals to 15?

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There are two combinations of numbers when multiplied together are equal to Asked in Math and Arithmetic How many different combinations can you make using 2 3 6 and 9? If you use them only once each, you can make 15 combinations. Asked in Math and Arithmetic, Factoring and Multiples What has a 3 digit number that is a factor of 5 and 8?

Asked in Math and Arithmetic, Statistics, Algebra What are the combinations of groups of 3 numbers using combinations of numbers 1 through 15 with no numbers repeating in a group?

The answer is Asked in Statistics, Algebra How many 4 digit number combinations are there using 6 numbers that can be repeated? Asked in Math and Arithmetic What does four sevens and a ace equal in cribbage how many combinations of 15? Six fifteens and a double pair royal equals Asked in Math and Arithmetic How many number combination can made from four numbers? In a combination, the order does not matter so that is the same as or etc. Assuming the 4 numbers are different, the correct answer is 15 comprising 4 1-digit combinations, 6 2-digit combinations, 4 3-digit combinations and 1 4-digit combination.

Another way to look at it is that the first number can be in a combination or not.How familiar is this situation: you have a large number of entries in a spreadsheet and you need to determine which ones add up to a particular amount? Personally, this occurs often as I frequently analyze spreadsheets full of data in the form of account transactions.

A task that would take as long as I could stand using trial and error now takes minutes thanks to the Solver Add-in. To determine this, go to the Data Tab of your spreadsheet and look for the Analysis section. If you do not see it, please enable it. If you are unsure of how to do this, please visit this site. Luckily, once you load this add-in you should never have to do it again. To begin, list all of the values of the individual entries in a column of the worksheet — name this column Data.

In this example I will be using column B. In the adjacent column, column C, enter the number 1 next to all of your values in column B and name this column Multiplier.

Lastly, in a third column, enter a formula that multiplies the first two columns. The spread sheet should look something like this click photo to enlarge :.

Once you have entered your data and added the two additional columns, the next step is to create an input cell for the value you are seeking. You will also need to include a cell which will sum all of products and a cell that will be the difference between the target number and the sum of the products.

See below for clarification. Finally, it is time to determine which data entries add up to your target number. The way this works is that the Solver either keeps the multiplier 1 or changes it to a 0. This then changes the product which affects the Sum of Products and Difference totals calculated in the previous step. The solver keeps testing combinations until the difference between the Target and Sum of Products is 0. However, there are two limitations to the solver: the solver limits the user to variables as well as constraints.

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After running this, the multiplier column is updated click photo to enlarge :.This article, I will talk about some methods to find which cells sum up to a specific value in Excel. Find and list all combinations that equal a given sum quickly and easily in Excel. Kutools for Excel 's Make Up A Number utility can help you to find and list all combinations and specific combinations that equal to a given sum number quickly and easily. Click to download Kutools for Excel!

Kutools for Excel : with more than handy Excel add-ins, free to try with no limitation in 30 days. Download and free trial Now! First, you need to create some range names, and then apply an array formula to find the cells that sum to the target value, please do with the following step by step:. Select the number list and define this list a range name-- Range1 into the Name Boxand press Enter key to finish the range name defined, see screenshot:.

After creating the range names, please apply the following array formula into cell B If you are confused with above method, Excel contains a Solver Add-in feature, by using this add-in, you can also identify the numbers which total amount equals a given value. Then in the To section, select Value Ofand enter your target value as you need. Under the By Changing Variable Cells section, please click button to select cell range B2:B9 where will mark your corresponding numbers.

And then click Add button to go to the Add Constraint dialog box, click button to select cell range B2:B9and select bin from the drop down list, see screenshot:. Click OK to go back the Solver Parameter dialog, then click Solve button, some minutes later, a Solver Results dialog box is popped out, and you can see the combination of cells which equal a given sum are marked as 1.

See screenshot:. Note : This method is also only can get one combination cells if there are more than one combination of values has a sum equal to the specific value.

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The first two methods are all complex for most of our Excel users, here, I can create a VBA code to solve this job quickly and easily. To get the correct result, you must sort the number list in descending order first.

And then do with the following steps:. VBA code: Find cells combination that equal a given sum:. Maybe all of the above methods are somewhat difficult for you, here, I will introduce a powerful-tool, Kutools for Excelwith its Make Up A Number feature, you can quickly get all combinations that equal to a given sum. Tips: To apply this Make Up A Number feature, firstly, you should download the Kutools for Exceland then apply the feature quickly and easily.

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After installing Kutools for Excelplease do as this:. Then, in the Make up a number dialog box, please click button to select the number list that you want to use from the Data Sourceand then enter the total number into the Sum textbox, see screenshot:.

And then, click OK button, a prompt box will pop out to remind you to select a cell to locate the result, see screenshot:. Then, click OKand now, all combinations that equal to that given number have been displayed as below screenshot shown:. Click to Download Kutools for Excel and free trial Now! Log in.

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Find all combinations that add upto given number

Please enter the email address for your account.Given a positive number, find out all combinations of positive numbers that adds upto that number. The program should print only combinations, not permutations. For example, for input 3, either 1, 2 or 2, 1 should be printed.

The idea is to use recursion.

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We use an array to store combinations and we recursively fill the array and recurse with reduced number. The invariant used in the solution is that each combination will always be stored in increasing order of elements involved.

That way we can avoid printing permutations. Exercise : Modify above solution to consider only distinct elements in a combination. This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to contribute geeksforgeeks.