## December 2018 - Challenge

You get an integer number as a challenge and your goal is to make it a square of an integer number.

To do that, you use two circles with four integers each.

You can change the number you got in steps. In each step we multiply it by the number in the bottom of one of two circles and rotate this circle clock-wise to its next number.

For example, if the two circles are [3,14,15,92] and [6,5,3,5] (the first number is initially at the bottom) then we can solve the input number 42 (i.e. make it a square) by multiplying as follows:

1st circle [3,14,15,92] 42*3=126 2nd circle [6,5,3,5] 126*6=756 2nd circle [5,3,5,6] 756*5=3,780 2nd circle [3,5,6,5] 3780*3=11,340 2nd circle [5,6,5,3] 11340*5=56,700 1st circle [14,15,92,3] 56700*14=793,800 2nd circle [6,5,3,5] 793800*6=4,762,800 1st circle [15,92,3,14] 4762800*15=71,442,000 2nd circle [5,3,5,6] 71442000*5=357,210,000 and getting a square (357,210,000 = 18,900**2).

BTW, There is a much simpler solution, can you find it?

Your challenge, this month, is to find two circles (with four numbers each) such that the same initial state will allow you to solve at least 2,187 different integers between 1 and 65,536.

To make the problem more interesting, you must not use "boring" circles. A circle is called boring if the set of solvable numbers using only this circle is closed under multiplication (i.e. if you can solve X and Y using only this circle, then you can also solve X*Y with it). In the example above, one of the circles (which?) is boring.

**Update 3/12: **a bonus '*' for two non-boring cycles that create a combined boring solution.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

*If you have any problems you think we might enjoy, please send them in. All replies should be sent to:* ponder@il.ibm.com

**Challenge:**
28/11/2018 @ 12:00 PM EST

**Solution:**
02/01/2019 @ 12:00 PM EST

**List Updated:**
03/12/2018 @ 12:00 PM EST

#### People who answered correctly:

***Alper Halbutogullari **(28/11/18 03:46 PM IDT)

**Bert Dobbelaere **(28/11/18 11:55 PM IDT)

***Arthur Vause **(29/11/18 12:53 PM IDT)

***Eden Saig **(29/11/18 11:35 PM IDT)

**Dominik Reichl **(30/11/18 12:35 AM IDT)

***Deane Stewart **(30/11/18 05:48 AM IDT)

**Lorenz Reichel **(30/11/18 11:08 PM IDT)

**JJ Rabeyrin **(01/12/18 12:01 AM IDT)

**George Lasry **(01/12/18 06:04 AM IDT)

**Hugo Pfoertner **(02/12/18 03:39 PM IDT)