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Digit Puzzle Solver

Problem Statement

Find all solutions where:

  • A 2-digit number multiplied by a 3-digit number equals a 5-digit number
  • All digits 0-9 are used exactly once across all three numbers
  • The first digit of the 5-digit result is 1

Solutions Found

The solver found 6 valid solutions:

Solution 2-digit 3-digit 5-digit Result Verification
1 27 594 16038 27 × 594 = 16038
2 36 495 17820 36 × 495 = 17820
3 39 402 15678 39 × 402 = 15678
4 45 396 17820 45 × 396 = 17820
5 52 367 19084 52 × 367 = 19084
6 54 297 16038 54 × 297 = 16038

Verification

Each solution satisfies all constraints:

Constraint 1: Correct Multiplication

All multiplications are verified to produce the correct 5-digit result.

Constraint 2: Unique Digits (0-9)

Each solution uses all digits 0-9 exactly once across the three numbers:

Example - Solution 1 (27 × 594 = 16038):

  • Digits used: 2, 7, 5, 9, 4, 1, 6, 0, 3, 8
  • All digits 0-9 present: ✅

Constraint 3: 5-digit Result Starting with 1

All results are 5-digit numbers in the range 15,000-19,999:

  • 16038 ✅
  • 17820 ✅
  • 15678 ✅
  • 19084 ✅

Key Observations

Multiple Solutions

  • The puzzle has 6 valid solutions, not just one
  • This demonstrates the richness of the constraint space

Duplicate Results

  • 16038 appears twice (solutions 1 and 6)
  • 17820 appears twice (solutions 2 and 4)
  • This shows different factor pairs can produce the same result

Range Analysis

  • 2-digit numbers: Range from 27 to 54
  • 3-digit numbers: Range from 297 to 594
  • 5-digit results: Range from 15,678 to 19,084

Mathematical Properties

  • All 5-digit results are in the 15,000-19,000 range
  • The smallest 2-digit number used is 27
  • The largest 2-digit number used is 54
  • Results are well-distributed across the valid range

Algorithm

The solver uses a brute-force approach:

  1. Iterate through all 2-digit numbers (10-99)
  2. Iterate through all 3-digit numbers (100-999)
  3. Calculate the product
  4. Check if product is 5-digit and starts with 1
  5. Verify all digits 0-9 are used exactly once
  6. Collect valid solutions

Files

  • solve_puzzle.py - Main solver program
  • PUZZLE.md - This documentation

Running the Solver

solve_puzzle-py.txt

python3 solve_puzzle.py

Conclusion

The conjecture that the first digit of the 5-digit number is 1 was correct. The puzzle has multiple valid solutions, each demonstrating the elegant constraint satisfaction where all digits 0-9 are used exactly once across the multiplication problem.

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Windows 11 License / Serial Number – How to transfer

Moving Your Windows 11 License to Another Computer

1. Verify Your License Type

  • Retail keys can be transferred.
  • OEM keys are tied to the original hardware—not transferable.
  • Digital entitlement licenses link to your Microsoft account and may auto-reactivate on new hardware.

2. Extract Your Product Key

Open an Administrator Command Prompt and run:

wmic path softwarelicensingservice get OA3xOriginalProductKey

If that returns blank, try in PowerShell (Admin):

(Get-WmiObject -Query 'select * from SoftwareLicensingService').OA3xOriginalProductKey

If still blank, you likely have a digital-only license—no key is needed; just sign in on the new PC with your Microsoft account.

3. De-register on the Old PC

In an elevated Command Prompt, run:

slmgr.vbs /upk

This uninstalls the key from the old machine, freeing up the license.

4. Install & Activate on the New PC

Option A: Command Line
Open Admin Command Prompt and run:

slmgr.vbs /ipk YOUR-25-CHAR-KEY-HERE
slmgr.vbs /ato

Option B: Settings UI
Go to Settings > System > Activation > Change product key, paste your key, and follow the prompts.

If activation fails, confirm you have a Retail license (Settings > System > Activation) or contact Microsoft support for a manual transfer.

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Benchmark Ubuntu

Launch the following GUI tool from the command line

sudo apt update
sudo apt install hardinfo
hardinfo
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Install Python3 on RHEL Servers

Make sure it's a RHEL Server

[haguxsndapp02 ~]$ cat /etc/*-release
NAME="Red Hat Enterprise Linux Server"
VERSION="7.9 (Maipo)"
ID="rhel"
ID_LIKE="fedora"
VARIANT="Server"
VARIANT_ID="server"
VERSION_ID="7.9"
PRETTY_NAME="Red Hat Enterprise Linux Server 7.9 (Maipo)"
ANSI_COLOR="0;31"
CPE_NAME="cpe:/o:redhat:enterprise_linux:7.9:GA:server"
HOME_URL="https://www.redhat.com/"
BUG_REPORT_URL="https://bugzilla.redhat.com/"

REDHAT_BUGZILLA_PRODUCT="Red Hat Enterprise Linux 7"
REDHAT_BUGZILLA_PRODUCT_VERSION=7.9
REDHAT_SUPPORT_PRODUCT="Red Hat Enterprise Linux"
REDHAT_SUPPORT_PRODUCT_VERSION="7.9"
Red Hat Enterprise Linux Server release 7.9 (Maipo)
Red Hat Enterprise Linux Server release 7.9 (Maipo)

Install Python3

sudo yum install epel-release
sudo yum install python36
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Touch ID Stopped working on MacBook

You need to reset your secure token.

sysadminctl -secureTokenStatus mlr
sysadminctl -secureTokenOff mlr -password - -adminUser Manamana -adminPassword -
sysadminctl -secureTokenStatus mlr
sysadminctl -secureTokenOn mlr -password - -adminUser Manamana -adminPassword -
sysadminctl -secureTokenStatus mlr

On a Mac, a Secure Token is a crucial account attribute that enables users to perform specific, system-level operations, particularly those related to FileVault encryption and system security. It's essentially a permission that allows a user to manage and decrypt encrypted data on the Mac.
Here's a more detailed explanation:

Purpose:

Secure Tokens are used to authorize users to manage FileVault, which is Apple's built-in encryption feature. This includes enabling and disabling encryption, as well as decrypting the system drive.

Refer: https://macpaw.com/how-to/mac-authentication-disabled#:~:text=If%20you%20see%20the%20error,an%20issue%20with%20iCloud%20Keychain.