In April 2011, Mdsuhair asked a question at the Chandoo.org Forums
This is a candidate for Solver.
This post will walk us through the solution to the problem using Solver. It uses Solver and screen shots from Excel 2007.
All versions of Excel have solver available. Users should note that the screen shots may not match your version although the functionality will, some of the functions appear in different locations in different versions of Solver.
What and Where Is Solver
What is Solver
Solver is an Excel add-in that can solve problems by enabling a Target cell to achieve some goal.
This goal may be to minimse, maximise, or achieve some target value.
It solves the problem by adjusting a number of input cells according to a set of criteria or constraints which are defined by the user.
Where is Solver
Solver is an Excel add-in supplied with Excel, but not enabled by default.
To enable solver
File, Excel Options, Add-ins, Manage Excel Add-ins, Select the Solver Add-in checkbox
Solver will now appear as a New Tab on the Data, Analysis Tab
Solver Example
This post is based around a worked example Solver Example File, the file is compatible with all versions of Excel.
Defining the Problem
Mdsuhair had a series of 8 Items each which had a value:
He wants to know which items should be combined so that the sum of the values of the items is nearly equal.
To do this we need to assign each item into a Bucket. Namely Bucket A and Bucket B.
We will put values of 1 into a Bucket for each Item to show that it is assigned to that Bucket and a value of 0 to show that the bucket is empty (In/Out) Value.
We can start by adding a Total Column, which counts items in Buckets A + Bucket B for each Item, It then totals the totals.
We also know that we need to work out the Value of each Item in each Bucket
We do this by multiplying the Items Value by the Buckets (In/Out) value
Finally we need to add up the values in each Bucket and work out the difference between them
Mdsuhair’s original problem was to minimise the difference between the sum of the values in the 2 buckets.
Now we can place values of 1 in the buckets manually and Excel will show us the value of each Bucket and the Difference between them in Cell G11.
I have applied some conditional formatting to show when a cell has a value > 0.
The problem is that there are 28 or 256 combinations of answers, and to test them all manually at 1 every 5 seconds would take 21.3 minutes, assuming we can keep up that pace and remember which was the best combination.
This is where solver comes to the fore.
Applying Solver
To apply solver we need to define a series of requirements, rules and constraints.
These requirements, rules and constraints guide solver and set limits which allow solver to quickly narrow in on the answer.
What are our rules
Our main requirement is to minimise the difference between the value of the 2 buckets.
The difference between the 2 buckets in our example is cell G11, the sum of Bucket 2 values minus the Sum of Bucket 1 values.
We want to have G11 as low as possible but greater than or equal to 0.
We also know that an item can only be in Bucket A or Bucket B, it can’t be in both and can’t be Broken apart.
That is 2 Constraints for each Item
Firstly The Total column must be equal to 1
Secondly the Buckets Values must be Integers
We also know that the Total Number of Items is 8, this is another constraint.
We will discuss how these constraints are used in the next section
The Solver Window
This section will explain the solver window and its use in defining the problem within solver.
A Blank Solver Window
A Filled Solver Window
Set Target Cell:
This is the Target cell which is the cell which you are trying to solve the problem for.
Our Target cell is G11, The difference between the 2 Buckets values
Equal To:
The Equal To: section defines what we want to do with our Target Cell.
We want to achieve the same value in each Bucket and so the difference between the Buckets will be 0.
It might sound strange but we don’t want to minimise that difference. A minimal value will be achieved when all the Items are placed in Bucket A, as our equation for G11 will then have 0 – Total which is –Total, which is more minimal than 0.
Another way to constrain this is to Change G11 to =Abs(G10-H10)
This allows us to use Min as an Equal To: Value
But for now we can just leave G11 as =G10-H10 and we will set the Equal To: section as 0.
By Changing Cells:
Changing Cells: refers to the cells which will be modified by Solver to try and solve the problem.
We want to let Solver change the number of items in each bucket, this is the range: $C$2:$D$9
Hint: You can try the Guess button next to the Range Reference and Solver will take a Guess at what cells the problem is dependent on.
Always check this if you use it, especially in complex models.
Subject to the Constraints:
Constraints are the rules which define the limits of the possible solutions to the problem
We will add several constraints for our rules:
1. The Total column must be equal to 1 for each Item
2. The Bucket Value must be an Integer
3. The total contents of the 2 buckets must be 8 items
4. You could add a further constraint that each Bucket should hold the same number of items
Hint: As a general Rule, Under Constrain rather than over constrain! You can always add more constraints later.
To do this we will use the Add Constraint Button
1. We need to add a constraint for each cell in the Range E2:E9 that it is only allowed to be = 1
This constraint must be applied for each cell in the range E2:E9
2. We need to add a constraint for each cell in the Range C2:D9 that it is only allowed to be an integer
This constraint must be applied for each cell in the range C2:D9
3. We need to add a constraint for the Total of the 2 Buckets, E10=8
You can Change or Delete Constraints if you make a mistake by selecting the appropriate constraint and using the Change or Delete Buttons
Save and Load Solves Parameters
Selecting the Options Button there is the Option to Save Model and Load Models.
Hint: The Save/Load Models has been shifted onto the main Solver dialog in Excel 2010.
Using the Save Model and Load Model options you can Save and the Load the Solver Parameters for your model. The Save Model saves the parameters in a Range of cells as shown below.
This allows an easy way to actually setup and/or change the solver parameters.
Hint: Setup one constraint using solver then Save the model. Edit the model on the worksheet and re-load the model as required.
Note: That the parameters although when saved show as True/False or Numbers are all Excel Equations, see above.
This means you can edit them to change the Constraints and Parameters as required and re-load them into solver.
I have included 3 sets of Parameters for our model.
These are:
- Base Case – Forces bucket values to be equal, Allows uneven bucket counts
- Equal Sized Buckets – Forces each bucket to contain the same number of items
- Force an error – Which forces an error in the solver model
Load each model and try them at your leisure.
Running the Solver Model
Warning: Solver is a computationally complex add-in, so once your model is setup, Save your Workbook.
Prior to running the model there are a few parameters we should look at to ensure the model solves correctly.
On the main Solver window select the Options button. (Some of these parameters are on the Main Solver window in Solver 2010)
Generally you can accept the defaults but in this case we will change the following
Assume Linear Model – Select
Assume Non-Negative – Select
Note: Solver in Excel 2010 will return a better answer without these 2 parameters enabled by default
The other 2 parameters which you may need to change from time to time is
Precision: Precision is a number from 0 to 1 and higher means more precise
Tolerance: Tolerance shows how far away from a Number, an Integer constraint is allowed to be
The use of the Estimates, Derivatives and Search parameters are beyond the scope of this post. I direct you to the Excel Help on these subjects, by selecting the Help button.
Run the Model
To Run the Model, select the Solve Button from the main Solver menu.
The main status bar in Excel will flash up a number of statistics about the internal workings of the Solver add-in. Generally these flash by and are too fast to read. If a model is too complex it may stall and you won’t see any movement for a while. Solver generally recovers from these problems itself.
Once the Solver model finishes it will display a dialog of the results and allow you to do several things
First thing to note is that “Solver Found a Solution“.
If it has found a solution, the worksheet cells will be changed to show the solution
You now have 4 options:
- Run a Report
- Save a Scenario
- Return to the model
- Check Your Results
Run a Report
Run a report by clicking the report you want.
A new sheet will be added to your workbook depending on the report but will be called:
- Answer Report 1,
- Sensitivity Report 1
- Limits Reports 1
etc.
Note, that not all reports are relevant at all times, depending on the Constraints you have applied.
Save a Scenario
Selecting the Save a Scenario button takes you to the Save Scenario dialog.
Type in a Name and the Scenario of your model is saved as a Scenario.
Scenarios as available for use in the Scenario Manager, which is accessed from the Data, What-If-Analysis Tab
Return to the model
You can return to your model and either:
- Keep Solver Solution
- Restore Original Values
Check the Results
Solver is probably the most Black Box’ish of systems within Excel. As such any results it puts out must be manually checked for suitableness before further use.
These checks for realness, should as a start confirm that the results meet all the criteria supplied.
Are the results roughly what were expected?
Are any Minimums or Maximums violated?
What If Solver Doesn’t Find a Solution?
From time to time Solver will return with an error that a “Solver could not find a feasible solution.”
When this happens it is indicating one of several possibilities:
- Your model is over or under constrained
- Your model constraints are impossible to meet
- Your model constraints have an error
Start by checking the current constraints for errors and ambiguities
Eg: in our case we have 8 items so requiring the Count of the two buckets to be 20 is impossible to meet
My Solver Answer has Strange Numbers?
In solver up to and including Excel 2007, solver would commonly return numbers like 3.5E-18.
This is 0.0000000000000000035, which is effectively 0
If your model returns these, feel free to go through the model and change them to 0, in our model we should also check as the corresponding 1, may in fact be 0.9999999999999999965.
It should be noted that this problem in Solver in Excel 2010 does not occur as often but will still occur.
What and How have you used solver in the past?
What and How have you used solver in the past?
Let us know in the comments below:
54 Responses
Hi Chandoo,
This is awesome *****
Found 6, just one remaining, and I think it should be in sheet2, as I found 1 in each sheet but didn’t found anything in sheet2 (till yet, I am keep looking).
Very cleaver and amazing work, enjoyed a lot…
Thanks Chandoo for this beautiful work.
Wish you have great time at Hyderabad.
Regards,
Khalid
go to AB201 on Sheet2, you will see Panda there !!!
Press F2 in Cell A1 and then read the actual text !!
In Sheet 2 go to Cell AB201. You will find one.
There is one on first sheet, if you press F5 (goto), the word PANDA can be seen there.
Oh I found the last one, (custom format hmm)
Truly Amazing and the beauty of this forum.
You are an Artist Chandoo.
Hi Chandoo,
Wow, you really have magical skills. I am in office and this sheet ate up an hour of my time….didn’t expect that.
I could find 5 of the 7 pandas. Didn’t know one could hide so much data in innocent looking excel sheets.
Thanks!
-Ranjith
yeah! found all 7 panda, time to go to china.
This was very fun and challenging, thanks for posting! I found all of them (well, Sheet1 was tricky, it seems you’re supposed to find the cell and type it in yourself?). Wasn’t sure if it was cool to post the answers here or not, though. Guess I’ll post SPOILER ALERTS so you can skip the rest of the message if you don’t want to see what I came up with.
SPOILER! SPOILER! SPOILER!
My answers appear below.
Sheet1: type PANDA in cell PAN3489
Sheet2: cell AB201
Sheet3: cell J8 (Picture1)
Sheet4: cell H9
Sheet5: expand Chart1
Sheet6: formula = “=MID(ADDRESS(9,2^3*23*59,4),1,3)&BIN2HEX(11011010)”
Sheet7: named range (A1:I18)
Wookie – I would love to get a walkthrough of HOW you figured out sheet 1 and a bit of a formula walkthrough for Sheet 6.
Basically, I don’t know how I could have found that particular cell input message on Sheet 1.
And I have no clue about the BIN2HEX part of the formula…before your hint I was able to get the output to read AN9DA. The change to MID and the addition of that ‘,1’ changed it to PANDA…
Hi Rachel,
To get to the cell in sheet 1 you can press: ctrl G. Then special and then data validation: all. This is also the way to find panda in sheet 7 😉
I agree, this was a fun way to test your ability to navigate through the functionality of Excel! And since you already posted the SPOILER ALERT warning, I should be safe posting a reply to your comment with some solutions of my own… 🙂
I found all the same solutions you did with a few minor changes:
Sheet1: If you notice, cell PAN3489 has Custom formatting. You don’t have to type “PANDA”, just the number 1.
Sheet6: The MID function works as you described, but you can also simply change the RIGHT function to the LEFT function without having to add in the start and end positions for MID.
Sheet7: Yes, the range name for these cells is called PANDA, but you don’t see the actual word in the sheet unless you change the Zoom setting to 39% or less (hence the clue “Z” 39%).
Thanks again for a great post, Chandoo!!
I must admit sheet 7 defeated me, but I have some corrections
Sheet 1 – you type =LEFT(ADDRESS(ROW(),COLUMN(),2),3)&DEC2HEX(ROW())
in PAN3489 to get “PANDA1”. As it is the first panda. I think panda1 is appropriate, but maybe
=LEFT(ADDRESS(ROW(),COLUMN(),2),3)&LEFT(DEC2HEX(ROW()),2)
is better, because it leaves you with “PANDA”
Sheet 6 – I corrected to
=LEFT(ADDRESS(9,2^3*23*59,4),3)&BIN2HEX(11011010)
Picky I know, but who uses mid when a right or a left will do?
I know; that was weird. I did try using a LEFT formula, but I kept getting the $ prefix from the cell address. So I tried a couple of variations using MID and it gave me the result I needed. This is actually the first time I’ve ever tried using a MID formula starting at the first character, but I wasn’t trying to spend a lot of time on it, so I went with what worked.
Sheet1: Type 1 in PAN3489
Sheet6: =LEFT(ADDRESS(9,2^3*23*59,4),3)&BIN2HEX(11011010)
Slight change…
For sheet 1 goto PAN3489 and type in 1. The word PANDA appears.
Love it!
Sheet 6 was my favorite. How many people still know what binary, hex and octal are? :o)
—–Spoilers———
Alternate Solutions
1) Type “1” (not the quotes) in PAN3489 and Excel will turn “1” into “PANDA”
6) The formula Wookie lists also works with LEFT in place of MID
Lot of fun. Solve time ~20 mins.
@ Rob
How this 1 turns to PANDA .. means How this is done by excel any formula or something in VBA
Also how to reach cell PAN3489 .. there are no clues given on sheet 1
You reach PAN3489 by pressing Ctrl + End to bring you to the last used cell in Sheet 1
@ Navdeep I found PAN3489 by going to “Formulas” and then “Name Manager” and saw there was a field called “Clue1” listed in the Name Manger that references 3489. Finding PAN as the column index was just a bit of a lucky guess through trial and error. Then a note in cell PAN3489 when you navigate there says to try “typing something.” I tried scrolling through the Format Cells menu to see if the text typed in the cell needed to be formatted a certain way, and noticed that “1= Panda” was listed in the custom text menu and tried it. A bit brute force, but I think the desired text entry.
Clever!
The Data Validation one took me a bit. Had to resort to brute force.
Thanks for the fun!
Awesome! Found 7 pandas in 20 minutes)))
Sheets 1 and 6 were the best!
Thanks!
Sheet 1: The answer is not type in Panda. Type 1. There’s a special formatting that replaces 1 with Panda.
Sheet 6: Just replace right with left, don’t worry about changing the numbers.
Sheet 7: I found the named range, but don’t know what the Z 39% means. Thoughts?
when you changed the zoom level to 39% or below, you will see the name of namedrange (if any)
WOW! I’ve just found the secret eighth PANDA!
Truly awesome!!!
Am I the first one who figured that out, guys?
Btw, thanks for the puzzle!
Found them all – very inventive. Had to think outside the “box”. Great fun!
It was truly a artists work
chandoo you are grate
all sheets are deigned different from each other
@Wookiee: you have a good for others by posting the answers, Thank you too
it is fun and great invent
Guys I Got 8 PANDA in the workbook… 🙂
[Look Chandoo has against played great trick by reserving one more ester egg, but we are also fan of none other than Chandoo, who can get hold of hidden 8th (untold) ester egg]
Here is the full list:
1) Sheet1: Type 1 in Cell PAN3489
2) Sheet2: Goto Cell AB201
3) Sheet3: Check the picture located above cell J8
4) Sheet4: Goto Cell H8
5) Sheet5: Cells, viz., A4, A10, A16, A21, A29 have all alphabets of PANDA
6) Sheet5: Resize the chart to see PANDA
7) Sheet6: Correct the formula as LEFT(ADDRESS(9,2^3*23*59,4),3)&BIN2HEX(11011010)
8) Sheet7: Range A1:I18 is named as PANDA
1) Sheet1: Type 1 in Cell PAN3489
2) Sheet2: Goto Cell AB201
3) Sheet3: Check the picture in the cell J8
4) Sheet4: Goto Cell H9
5) Sheet5: Resize the chart to see PANDA
6) Sheet6: Correct the formula as LEFT(ADDRESS(9,2^3*23*59,4),3)&BIN2HEX(11011010)
7) Sheet7: Range A1:I18 is named as PANDA
Actually, for sheet7, if you set the zoom to 39% or less, you will see the word PANDA. Yet another PANDA! 🙂
Hi,
i want to know how to manage bill wise manage vendor invoice and payment in excel please suggest.
Thanks,
Ram
Hi Chandoo!
You rock with these amazing skills!
Sheet 1: ??
Sheet 2: ??
Sheet 3: Cell J8
Sheet 4: Cell H9
Sheet 5: A4, A10, A16, A21, A29
Sheet 6: B2
Sheet 7: ???
Sheet1 F5
Sheet2 AB201
Sheet3 Picture1
Sheet4 H9
Sheet5 Chart
Sheet7 Zoom to 30%
I love this time of year and look forward to Chandoo’s egg hunts. Whilst I got all the pandas, I do not understand how sheet 7 works; Where is the source data and why does it only work when zoomed out to 39% or more?
@Leon-K
When you change the zoom level to be less than 40% Excel shows the Ranges which have Names applied to them
Ha ha, that’s fantastic. Thanks Hui. @Chandoo, thanks for yet another method to decrypt worksheets in order to re-build or explain them better to clients.
These were fantastic and kept me intrigued until I could finish them. (Had to look here for help with Sheet1!) Definitely learning a lot about some new formulas. Awesome, Chandoo!
Ok, just saw the notes on the Zoom 39% on Sheet 7. Can someone explain what’s happening here and why PANDA shows up at that level?
@Bryan
When you change the zoom level to be less than 40% Excel shows the Ranges which have Names applied to them
Wow, great exercise.
Tried and solved 5 out of seven and other two solved incorrectly (1 & 6).
Thanks 🙂
Hi Chandoo,
Gr8 …had fun in searching it. I got 5 out of 7.
You are brilliant.
Found all except in sheet6 as not able to understand formula.
thanks
Raja Aurongzeb
Hi,
I am not able to find 1st Panda, which is on Sheet1. Rest all I have found.
Wonderful Chandooji… you are brilliant.
Wow.. Awesome set of puzzles Chandoo!!
Am now trying to figure out how sheet 7 was prepared.. 39% Zoom setting logic.. Can someone help me with a hint?
Thanks!
Looks like this is an XL feature.. Zooming out the worksheets below 40% level, by default displays all named ranges (more than 2 cells)! Had not come across this till date..
Great works! Was having FUN in finding the pandas. Thanks.
btw, I used one basic function (Find, CTRL+F) to find 2 pandas. Simply Find “Panda” within “Workbook”… To my surprise, seems no one mentioned that in the process.
On other other hand, Selection and Visibility Pane is a handy tool to see if there is “extra” shapes for locating pandas hidden in chart/picture.
Had fun doing this, Found 5 and the rest I saw clues on here 🙂
I really enjoyed when finding the pandas.And also I am so surprised.Very Nice thought and Excellent.
This was fun! Thanks!
Nice and fun post. Thanks, Chandoo!