Pattern hunt
- How old are you?
- 45. Why do you ask?
- Do you know how much 45×45 – 1 is?
- 2024, if I am not mistaken.
- You are not mistaken.
- Good!
- If you only had two fingers how would you express 2024?
- You mean in binary?
- Oh, sorry, I forgot you are educated!
- 2024 = 11111101000 in binary.
- That was fast!
- I just Googled it by typing “2024 in binary”.
- Do you notice anything about the result?
- It is much longer than 2024.
- Anything else?
- No.
- OK. Here is the challenge. Express n times n minus 1 in binary, discover a pattern, and prove it.
- What is n?
- Any number.
- That seems hard!
- Above you see some data created with Open Office Calc using the Base(x;2) function.