## Ask Professor Puzzler

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Good morning Puzzling Friends! I have a puzzle for you all.

rinku sends us the following question: "How can we get one using the numbers 1 to 10 in the same order using the four operations?"

This is all we have for details on this puzzle. It is not clear, from the wording, whether parentheses are allowed.

For example, are you allowed to do things like this: 1(2 + 3 - 4) + 5... etc. If you can use parentheses, that simplifies the problem, I'm sure!

I'm curious to see how many *different* solutions we can come up with. Try doing it without parentheses, and if you can't solve it, try it with parentheses. Use the "Ask Professor Puzzler" link at the bottom of the page to submit your answer.

I'll update this blog post with the first/best submissions, so make sure you check back next week to see what solutions have been shared!

The only solutions which were posted were variations on a single theme.

It occurred to me, as I looked at this, that each pair of successive integers had a difference of one (or negative one, depending on which way you do the subtraction). Thus, if we alternate adding and subtracting differences, we'll get the desired solution:

First we add 2 to -1.

Then we subtract 4 from 3.

Then we add 6 to -5.

Then we subtract 8 from 7.

Finally, we add 10 to -9.

-1 + 2 +3 - 4 - 5 + 6 + 7 - 8 - 9 + 10 = 1

The other solutions received were simply variations on the add and subtract differences concept, such as:

1 - 2 + 3 - 4 - 5 + 6 - 7 + 8 - 9 + 10 = 1.

Many other variations are possible.

Can you find a solution that includes operations besides addition and subtraction? Use the "Ask Professor Puzzler" link to give us your solution!