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1000! Challenge

This contest is a little different from other contests I've run. It's different in that it is being sponsored by a Guest Host who has created the problem and who is providing the prizes. If anyone else would like to Guest-Host a contest in the future, please contact me.

The Guest Host for the Kamenetsky 1000! Challenge is â€¦ (wait for the surprise) â€¦ Dmitry Kamenetsky.

This contest is identical to the recent Factorials contest, with a few exceptions. If you are not familiar with the Factorials contest you should read its description now, otherwise very little below will make any sense to you.

The ways in which the Kamenetsky 1000! Challenge differs from the Factorials contest are:

• The values of n are different.
• The notation for submitting solutions is different.
• The scoring system is different.
• The contest is shorter.
• The groups.io rules are different.
• The prizes are different.

Which values of n?

Just n = 1000. No other values.

What is the notation?

Instead of listing k+1 terms for a k-step solution, you will list k steps. For example, let's supposed you've created the 7-step solution (1, 2, 3, 6, 4, 24, 5, 120). In the Factorials contest you would have submitted the 8 terms:

``` 1, 2, 3, 6, 4, 24, 5, 120 ```

In this contest you would instead submit 7 steps for generating all but the first term:

``` 0+0, 0+1, 1*2, 0+2, 3*4, 0+4, 5*6 ```

Each step is in the form a◊b, which means take the ath term (0-based) and combine it with the bth term using operation ◊ (+, - or *). Recall that the 0th term is always 1.