- #1
Rahmuss
- 222
- 0
1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, _, _, _
What are the three blanks? And why?
What are the three blanks? And why?
Discover the Pattern: 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4
- Thread starter Rahmuss
- Start date
In summary, the numbers 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, _, _, _ represent the last digits of squares, with the next three numbers being 9, 6, 5. The differences between two are antisymmetrical and can be represented as 3, 5, -3, -1, | 1, 3, -5, -3, -1 | 1, 3, _ _ _ if you flip and invert the signs. This pattern continues for the next five sets.
- #2
BicycleTree
- 520
- 0
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
Atrus
- 19
- 0
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
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
Rahmuss
- 222
- 0
Atrus said:
LOL... that's pretty funny... I didn't even notice that.
The answer I was looking for was given by BicycleTree.
- #5
Atrus
- 19
- 0
Rahmuss said:LOL... that's pretty funny... I didn't even notice that.
The answer I was looking for was given by BicycleTree.
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
ArielGenesis
- 239
- 0
do atrus's answer match with bicycletree answer, for the next 5 sets?
- #7
Atrus
- 19
- 0
ArielGenesis said:
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
ArielGenesis
- 239
- 0
what a great co incidence ^^
FAQ: Discover the Pattern: 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4
What is a "Somewhat Simple Pattern"?
A "Somewhat Simple Pattern" is a recurring and recognizable arrangement or sequence of elements that is not overly complex or difficult to understand.
What makes a pattern "somewhat simple"?
A pattern is considered "somewhat simple" when it is not overly complicated or difficult to comprehend. This can be because it is made up of familiar elements, has a predictable sequence, or is easy to recognize and reproduce.
How can patterns be used in science?
Patterns are used in science to identify and explain natural phenomena, make predictions, and help organize and understand large amounts of data. They can also be used to create models and theories that help us understand the world around us.
Are patterns only found in science?
No, patterns can be found in all areas of life, including art, music, literature, and even in our daily routines. They are a fundamental part of how we perceive and understand the world.
Why is it important to study and understand patterns?
Studying and understanding patterns helps us make sense of the world and can lead to new discoveries and advancements in various fields. It also allows us to make predictions and recognize patterns in new situations, which can be useful in problem-solving and decision-making.