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Unique Values across multiple columns

I have a spreadsheet that has multiple values in it, but I need to create a formula that would pull the names from the columns without any duplicates. Here's an example spreadsheet:

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I would like the result to be like:

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So to do it manually, I'm using a SUMIF to search the data for "Walked dog" and add the value.

I'm doing this by manually typing the event names, and if there's one added, I have manually add this instead of something automatically adding that new unique value to the spreadsheet. I've tried SUBTOTAL, SUBPRODUCT, and SUMIF, but they don't seem to do what this spreadsheet requires. Any help would be appreciated.

=SUMIF($C:$F,"Walked dog",$D:$F) is the only function I can get to work correctly, but that requires manual input of the names each time a new event is added.

If you are able to get all your data into one column, you could then use a pivot table. Pivot tables would allow your "Time" column to be grouped and summed up by your "Event" column. As I mentioned, you would need all your "EventN" columns copied into a single "Event" column. You will often need to transpose your data around to make your life easier when using spreadsheets.

Here's the first google result for an example: http://www.excel-easy.com/data-analysis/pivot-tables.html

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