Question

If i take any 3 diggit number and subtract 5. Multiply result by 7. Add 33. Multiply the result by 11. Add 22. Multiply result by 13. I should have original three digits repeated twice in a six digit number. Is there a pattern is to why the three digit number is repeated twice in a 6 digit number?

Any 3 digit number can be from 100-999.

Answer 1

its pretty cool, as to why there is the pattern.... i dont know
there are a lot of patterns in our number system that can be found or manipulated to do neat things

Answer 2

it;s similar to my previous question. But on this one how do i explain why this happens?

Answer 3

Let the starting number be x
subtract 5: (x-5)
multiply by 7: (x-5)*7 = 7x - 35
Add 33: 7x - 35 + 33 = 7x - 2
Multiply by 11: (7x - 2) * 11 = 77x - 22
Add 22: 77x - 22 + 22 = 77x
Multiply by 13: 77x * 13 = 1001x

1001x = 1000x + x
Multiplying a 3 digit number by 1000 shifts it to the left 3 places.
Adding the three digit number to the above repeats the 3 digit number twice.

Answer 4

Example: x = 538
We proved above that doing all the arithmetic results in multiplying the three digit number by 1001 which can be 1000 * the number + the number
1000 * x = 538000
1000x + x = 538000 + 538 = 538538

Answer 5

that makes more sense!