# Somewhat Simple Pattern

1. May 23, 2005

### Rahmuss

1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, _, _, _

What are the three blanks? And why?

2. May 23, 2005

### BicycleTree

The numbers are the last digits of the squares. The next squares are 169, 196, 225, so the next numbers are 9, 6, 5

3. May 23, 2005

### Atrus

Next three are 9, 6, 5. Differences between two are antisymmetrical

3, 5, -3, -1, | 1, 3, -5, -3, -1 | 1, 3, _ _ _

If you flip marked section, and invert the signs, you get 1, 3 (already there) and then 5, -3, -1.

Last number was 4 so
4
+5 = 9
-3 = 6
-1 = 5

4. May 23, 2005

### Rahmuss

LOL... that's pretty funny... I didn't even notice that.
The answer I was looking for was given by BicycleTree.

5. May 23, 2005

### Atrus

I was pretty surprised that this one had two answers. But probably a number theorist wouldn't be. And I'll leave it to one to prove the answers are equivalent ;)

6. May 24, 2005

### ArielGenesis

do atrus's answer match with bicycletree answer, for the next 5 sets?

7. May 24, 2005

### Atrus

Yes they do! :) Sequence of differences is 1 3 5 -3 -1 (first number in line being 0), then you flip it and change signs to get 1 3 -5 -3 -1. And then you do it again, so initial sequence appears. As you can see, only the middle number's sign (+-5) is changed. And it fits quite nicely to series of squares... next five numbers would be 6 9 4 1 0, according to both explanations :) It has been some time that I've taken discrete mathematics course, so I'm a bit rusty in number theory to prove the equivalence. Still, the challenge stands :)

8. May 25, 2005

### ArielGenesis

what a great co incidence ^^