Molecular Weights 8

I wouldn’t normally publish a post on such an esoteric topic as this. However, since the idea for it came as a result of a challenge posed by the venerable David Hager, I felt that I could not resist.

And that challenge was as follows: given a list of chemical elements and their respective atomic weights, a formula to determine the weight for a given molecule.

It goes without saying that there are numerous quick and easy online applications which will perform such a calculation. Nevertheless, and however unlikely it may seem, there is still a small probability that this post will reach one or more of the tiny minority who have a practical need for such calculations to be performed within Excel (and, in addition, perhaps without recourse to VBA).


Shortest Formula Challenge #6: Results and Discussion Reply

A couple of weeks ago I set readers the challenge which can be found here.

Once again, some truly excellent responses and a noticeably collaborative attempt towards obtaining our final, minimal-length solution. So many thanks to all who contributed: Alex, John Jairo, Lori, Snakehips and Will!

And that solution, at 108 characters, is:


How does it work?


Advanced Formula Challenge #12: Results and Discussion 2

Last week I set readers the challenge which can be found here.

Such was the number and variety of responses to this challenge that presenting a detailed breakdown of one such solution – as has been the case for all of the first eleven in this series of challenges – would, I feel, be somewhat inappropriate.

For the majority of these challenges, it could be argued that there has been one solution which is indisputably “better” than the rest. Perhaps such an adjudication can also be made here, though to do so would certainly not be a straightforward exercise. What’s more, to pick just one of the many solutions would be to leave the rest – unfairly in my opinion – left on the sidelines.

As such, I would refer the readers to the many solutions in that post and to enjoy dissecting the varied and wonderful constructions therein. And to simply thank all those – Alex, aMareis, Maxim, John Jairo, sam, Jeff, Lori, Ron, Michael, Christian and XLarium – whose excellent contributions led to such a fruitful and inspiring discussion.

There’s evidently still much to be discovered in the world of worksheet formulas!

Another challenge to follow shortly. Watch this space!

Simultaneous Locating of First and Last Numbers in a String 23

I was initially debating whether to give this post a more pragmatic title, such as “Extracting Phone Numbers from a String”, that being one of the more common practical applications for the techniques outlined here.

However, the extraction of phone numbers (I’m referring here to that type which employs some form of delimiter, e.g. 1-800-12345, and not that which comprises a non-delimited numerical string, e.g. 180012345, there existing already well-documented formula techniques for the extraction of the latter – although of course the set-up given here will work for those as well) is certainly not the only use for this method, and so, in the end, I chose to go with a less restrictive, more theoretical title.


Extracting Numbers of Set Length Only from Alphanumeric Strings 18

In this post I would like to present a solution to the practical problem of extracting a number of defined length from an alphanumeric string which may contain several numbers of varied lengths.

Indeed, the inspiration behind this post is in part derived from having personally witnessed many such requests on the various Excel forums, most of which involve the extraction of e.g. an account number of fixed length, 6 digits, say, from a longish string containing many other numbers.

As an example, given the following string:

20/04/15 - VAT Reg: 1234567: Please send 123456 against Order #98765, Customer Code A123XY, £125.00

we may wish to extract the one occurrence of a 6-digit number (123456) from that string.


Shortest Formula Challenge #4: Results and Discussion 4

Last week I set readers the challenge which can be found here.

A good response to this one, leading to a solution for which, in the end, most people who responded can take some credit.

Snakehips started the ball rolling with a nice logical construction involving “OR”ing two separate COUNTIFs; John Jairo V then shaved off several characters from this solution; this was then further refined by Elias; and, finally, after several attempts at constructing a solution using FREQUENCY, Alex Groberman took the COUNTIF set-up and wrapped it in that most wonderful of functions – MODE.MULT – to give us our winner.


Counting Rows Where Condition Is Met In At Least One Column 39

In this post I would like to present a solution to the situation in which we wish to count the number of rows for which a stipulated condition is met in at least one of several columns.

To illustrate what is meant by this, consider the extract below:

Counting Rows Where At Least One Condition Is Met

which details levels of scrap nickel exports for various countries and for various years (you can download the workbook here).


Return Entry Corresponding to Maximum Value Based on Conditions 32

We are often faced with the practical situation in which we need to return the entry from a certain column which corresponds to the maximum numerical value from another column subject to one or more conditions.

For example, from the table below:

INDEX_MAX_IF Non-array Alternative

we may wish to return the date (column C) which corresponds to the latest version (column B) for a given order number (column A), where by “latest” we mean “largest numerically”.


Advanced Formula Challenge #11: Results and Discussion 11

Last week I set readers the challenge which can be found here.

Good results for this one: six answers received, six correct answers received – from Oscar, Daniel, diondan1, Bill, Ikkeman and Calvin. Plus one (unverifiable, though no doubt correct!) Google Sheets solution from Isai, as usual. 🙂

So congratulations to all of the above!

The majority of those solutions adopted a strategy of comparing the characters from two sets of arrays derived using MID over an array of start_num parameters, though a couple of solvers (Bill and Calvin) decided to first derive the ASCII codes for these characters and instead use these as the basis for the comparison.


Which numbers add up to total? (2): Multiple Solutions 8

Note to readers: this post has been updated due to the inclusion – at the request of Torstein – of a further version of this solution, in which the number of values to be considered is dynamic and so may be set by the user. This version may be found at the very end of this post.

This post, inspired by a question from Patrick MacKay, from Belgium – thanks, Patrick! 🙂 – is a (rather belated) follow-up to that which I made here, in which, to recap, I presented a formula-based set-up which, given a target figure plus a series of values, determined which, if any, combination of those values had a sum equal to the target.

The only slight drawback to that solution was the caveat that, if more than one combination of values existed which satisfied that condition, then only one of those combinations was given.

Here I would like to improve upon that set-up by presenting a refined version which will return all such combinations. What’s more, at the very end of this deconstruction I will give a further version of the solution in which the number of values to be considered is a variable which may be set by the user.

In fact, that early post was also one of the very few in which I did not give an explanation as to how the solution works, which I would like to do here.

As an example of the output, imagine that our target value – £1054.35, for example – is here in A1, and that we have a list of 10 values in A2:A11, as below:

Which Numbers Add Up To Total (Multiple Solutions)


Shortest Formula Challenge #3: Results and Discussion 1

Last week I set readers the challenge which can be found here.

This one provoked quite a bit of debate, and not all of it Excel-related! As I already have to several readers, I must again apologize for the lack of realism and statistical know-how inherent in the premise for this challenge, which was evidently constructed more with the required formula-work in mind than with any serious thought to methods in demography.

Still, at least some fascinating and impressive Excel work came out of it all, so perhaps my poor groundwork is somewhat forgiven, at least retrospectively!


Advanced Formula Challenge #9: Results and Discussion Reply

Last week I set readers the challenge which can be found here.

One correct solution received, courtesy of Lori, who not only presented a fine construction for working in Excel 2010 and earlier, but also a 2013 version, which had the added benefit of taking advantage of some of the new (and evidently very useful) features of that version to noticeably abridge the required set-up. So many thanks to Lori for sharing this knowledge and also congratulations on an excellent solution to a particularly complex challenge!


Advanced Formula Challenge #8: Results and Discussion 2

Last week I set readers the challenge which can be found here.

At the time of writing (Saturday morning, UK time; apologies if anyone has submitted something after that date), two correct solutions received (or three if you count non-Excel-based ones: as he has done for most of the recent challenges, Isai Alvarado produced a solution applicable to Google Sheets, which, as usual, I am unable to verify! So I’m taking your word for it that it’s perfectly correct, Isai! 🙂 ).

The two correct entries came courtesy of Snakehips, who gave a rather lengthy but perfectly correct solution, and John Jairo V, who improved upon his earlier attempt by producing a solution which, in essence, used a similar approach to Snakehips’ but which made use of some very nice technique involving MMULT to considerably abbreviate the required construction. Great work, John!


Advanced Formula Challenge #7: Results and Discussion 1

Last week I set readers the challenge which can be found here.

This is a trickier problem than it at first appears, and indeed there are several pitfalls which prevent us from using more “standard” techniques to arrive at a solution.

Perhaps the two main (hidden) obstacles, which were not immediately obvious from the examples I gave, are, firstly, the fact that we are prevented from using a construction involving a SEARCH-approach (e.g. by locating occurrences of each substring of the four types *????*, †????*, *????† and †????†, as John Jairo V attempted), since this of course presumes that there is only one occurrence of each of those substring types within our string, a presumption which cannot be made.



We sometimes look for non-array (i.e. non-CSE) versions of constructions which would normally require array-entry. Our reasons for doing so may be varied:

1) We may feel that it improves spreadsheet performance (sometimes true, sometimes not)

2) We perhaps have a dislike for having to use the required keystroke combination necessary for committing array formulas

3) We may simply be interested from a theoretical point of view


List of unique entries from column of space-separated strings 3

Given the list below in A1:A10, we may wish to create a list of unique, single words from that list, as per column B here.

Unique From Space Separated

We can do this with the following set-up: More…

COUNTIFS: Multiple “OR” criteria for one or two criteria_Ranges 58

In this post I would like to clear up what appears to me to be a rather widespread misunderstanding of how COUNTIFS/SUMIFS operate, in particular when we pass arrays consisting of more than one element as the Criteria to one or even two of the Criteria_Ranges.

This latter technique is used when the criteria in question are to be considered as “OR” criteria, which is not to be confused with cases where we wish the criteria passed to be calculated rather as “AND” critieria.

For example, given the following data:


Advanced Formula Challenge #5: Results and Discussion 5

Last week I set readers the challenge which can be found here.

This is a reasonably complex problem, and certainly so if we want to present a solution which is relatively concise. However, despite its complexity (and arguably lack of practical use), the solution demonstrates some important techniques for working with strings, and so is not without merit.

The required set-up is as follows:


Advanced Formula Challenge #2: Results and Discussion 2

Last week I set readers the challenge which can be found here.

Three solutions were offered, two of which from the same person, and both of which were correct! So many congratulations to Bill on successfully solving what was quite a complex challenge!

Indeed, as Ben Schwartz pointed out, this challenge appears to have been set previously on the internet, and seems to have been only partially solved on those occasions. In any case, thanks also to Ben for his suggestion, which he confesses was cobbled together from those previous solutions he found, and which worked in all but a few exceptional cases.