It seems spreadsheets & dinosaurs on a collision course. How else can you explain Jon’s XKCD Velociraptor problem solved with Excel and now this. *Debby*, an alert reader of our blog sent me this email yesterday.

I need an algebraic formula to solve this in Excel

I have 5 heads, 5 bodies, 4 arm sets, 4 leg sets and 3 tails. I need to see if I can create 1000 dinosaurs from these, and if that’s too many AND I need the 5 digit groupings to prove it and create them.

basically Xa*Xb*Xc*Xd*Xe=1000 – I’m not supposed to go over 1200. […] And then I want the 5 digit combinations if possible – right now they are trying to do the combinations by hand – would be awesome if we could do it in Excel.

### Ladies & gentlemen, let’s fire up Excel

There are two problems to solve.

(1) How many dinosaurs can be made?

(2) Listing of all such dinosaurs.

The first one is easy.

We just multiply the number of heads, bodies, arms, legs & tails. I know this sounds biologically impossible. But in math everything is possible. So we get =5x5x4x4x3 = 1200

That means, given the body part variations, we can generate 1,200 dinosaurs. Some of them may be hideous, but 1,200 of them nevertheless.

### Making 1200 dinosaurs in Excel

This is very simple. We just use the MakeDinosaur() formula in Excel.

Of course, I am kidding. There is no MakeDinosaur(). Instead, we can use the all powerful INDEX().

Let’s say, we have listed the various parts in a range like this:

Now, each of those ranges are conveniently named as *heads, bodies, arms, legs *and* tails*.

Next, in an empty column, we list 1200 running numbers. *Side note: we could do away with this step and use ROWS() function. But dinosaurs don’t mind helper columns.*

Let’s say, these running numbers are in H4:H1203.

We now use our T-rex sized INDEX formula.

=INDEX(heads,(H4-1)/240+1) & INDEX(bodies,MOD((H4-1)/48,5)+1) & INDEX(arms,MOD((H4-1)/12,4)+1) & INDEX(legs,MOD((H4-1)/3,4)+1) & INDEX(tails,MOD((H4-1),3)+1)

This generates all combinations of dinosaurs.

Let’s dissect the t-rex. Shall we?

- The formula is a concatenation of five INDEX functions.
- Each fetching one body part
*viz*head, body, arm, leg or tail

#### Head portion:

**Formula:** INDEX(heads,(H4-1)/240+1)

**What it does?** There are 5 head choices and 1200 possible dinosaurs. That means, each type of head is attached to 240 (1200/5 = 240) dinosaurs.

So, we simply take the number in H4, divide it with 240 and figure out which head to use.

#### Body portion:

**Formula:** INDEX(bodies,MOD((H4-1)/48,5)+1)

**What it does? **So we now have 240 possible dinosaurs with a given head. And we have 5 types of body. That means 48 dinosaurs per each type of body *given a head type. *

We could use INDEX(bodies, MOD(H4-1,240)/48 +1) to get the corresponding body number.

Alternatively, we can use the simplified version INDEX(bodies,MOD((H4-1)/48,5)+1)

**Why does it work? **That is for you to figure out. There is a reason we are not extinct yet.

**Remaining parts:**

We use similar logic to fetch other body parts.

### Download the dinosaurs

Download the 1,200 dinosaurs. Be careful, #14321 is a bit loony. She almost bit my shift key.

### How would you make ’em dinosaurs?

Of course, we could use VBA, other formulas to make these nasty reptiles. What would you do if someone asks you create a few dinosaurs? Share your recipe in the comments.

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## 6 Responses to “Make 1,200 dinosaurs in no time with Excel [formulas]”

Hello,

I am looking for a VB code to not copy a cell value based on the value of another cell in excel.

Example:- Need to not copy cell A1 value if B1 is blank .

If double click in cell B1 then A1 value is copy and if feed any value no need to copy A1.

And also no need to copy A2 value if D1 is blank. If double click in D1 then A2 value is copy and if feed any value in D1 then no need to copy A1 value.

I will just hardcode use VBA:

Sub MakeDinosaur()

Application.ScreenUpdating = False

Dim r, Heads, Arms, Legs, Tails As Integer

r = 4

For Heads = 1 To 5

For Bodies = 1 To 5

For Arms = 1 To 4

For Legs = 1 To 4

For Tails = 1 To 3

Cells(r, 1) = Heads & Bodies & Arms & Legs & Tails

r = r + 1

Next

Next

Next

Next

Next

Application.ScreenUpdating = True

End Sub

I agree with Sunny, his VBA solution is easy to understand and audit. One thing that bothers me is the DIM statement

Dim r, Heads, Arms, Legs, are Dimmed as VARIANT

Only Tails is Dimmed As Integer

Better DIM all these variables as LONG. Why? read more:

http://www.spreadsheet1.com/vba-development-best-practices.html

Hi Petros, my VBA is, at most, average. I made the mistake of assuming all are DIM as INTEGER by merely separating them using commas in a single statement. Your are absolutely right about the Variant part. I normally don't even bother to DIM at all although I am aware that it is a good practice to do so. Thanks for your valuable advice.

I did mine the same way Chandoo did it, although I used looked up each body part in a separate cell so to get the same output I would have to concatenate the five columns.

I used a similar method of generating permutations to work out all the 362880 possible permutations of numbers . Ie 123456789,

123456798, to 987654321.

It meant that I had every possible solution to the "Suko/Sojiko" puzzle. It meant that with the addition of a few helper columns which add four columns, I was able to find the solution by filtering the list.

Not only can I find a solution quicker, but I can verify it is the only possible solution - I have in the past come across puzzles which have more than one solution.

Hello,

I have another approach without using Index formulas. Also it doesnt need the matrix of the legs. (also i would prefer references instead of hard coded numbers)

Unfortunately i have no idea if calculation is faster with or without using the formula Index.

=ROUNDDOWN((ROW()-1)/240;0)+1&MOD(ROUNDDOWN((ROW()-1)/48;0);5)+1&MOD(ROUNDDOWN((ROW()-1)/12;0);4)+1&MOD(ROUNDDOWN((ROW()-1)/3;0);4)+1&MOD(ROW()-1;3)+1