Math Trick Puzzle: Amuse Your Nephew with This Trick!

[Mark44]

From a thread by @Harsha Avinash Tanti that was closed. This is an interesting puzzle, so I have started a new thread with the puzzle posed in the other thread.

How about this one,
I use this as magic trick to amuse my nephew

I think of any number between 20000 and 30000
say 29547 then I put in an envelop (1a)
then
I give a number 9549 (1b)
then I ask for a random number from my nephew suppose he says 2347 (2a)
then I say a random number 7652 (2b)
then I ask for another random number and he says 4587 (3a)
then I say a random number 5412 (3b)

then I tell him to add it all up vol-ah you get 29547. (4)

What trick have I used?

I have added numbers (in red) to help with the explanation. The numbers were not in the original post. Here's how the trick works.

You say a number (step 1a), which you put into an envelope.
The number in step 1b is the lower four digits of the number in 1a, plus 2.
In the example above, 29547 was the first number, so the number in step 1b is 9547 + 2, or 9549.

Step 2a--the nephew picks a number.
Step 2b--you choose a number so that when each digit of your number is added to the nephew's number, you get 9. In the example above, the nephew piced 2347, so you pick 7652. Note that these two numbers add to 9999.

Step 3a
Step 3b -- Same as steps 2a and 2b

Step 4. Add the numbers in steps 1b, 2a, 2b, 3a, and 3b, and you get this:
9547 + 2 + 9999 + 9999 = 9549 + 20,000 - 2 = 29547, the number in the envelope.

and can you do it for number range 50000 to 60000

I'll let others weigh in for that one.

 

[QuantumQuest]

9547 + 2 + 9999 + 9999 = 9549 + 20,000 - 2 = 29547, the number in the envelope.

So, essentially what he (EDIT: the OP of the puzzle) is doing - regardless of numbers picked, just account amounts back to the missing part.

 

[QuantumQuest]

I'll let others weigh in for that one.

I don't know if I think it right but as I don't see any constraint on the number of digits for the number that complements the number that the nephew gives, if you again take the four lower digits add 2 and take care to pick numbers that sum up to 24999 with the number that nephew gives, you get the original number again.

 

[mfb]

So, essentially what he is doing is - regardless of numbers picked, just account back to the missing part.

Exactly. "Think of a number, I'll tell you how much you have to add to get the number I wrote up previously" is not a particularly impressive mathematics trick.

Also, what happens if the other one chooses 64621? Do you pick a negative number?

 

[Mark44]

Also, what happens if the other one chooses 64621? Do you pick a negative number?

It's not stated, but the other person has to pick a four-digit number.

 

[Harsha Avinash Tanti]

From a thread by @Harsha Avinash Tanti that was closed. This is an interesting puzzle, so I have started a new thread with the puzzle posed in the other thread.I have added numbers (in red) to help with the explanation. The numbers were not in the original post. Here's how the trick works.

You say a number (step 1a), which you put into an envelope.
The number in step 1b is the lower four digits of the number in 1a, plus 2.
In the example above, 29547 was the first number, so the number in step 1b is 9547 + 2, or 9549.

Step 2a--the nephew picks a number.
Step 2b--you choose a number so that when each digit of your number is added to the nephew's number, you get 9. In the example above, the nephew piced 2347, so you pick 7652. Note that these two numbers add to 9999.

Step 3a
Step 3b -- Same as steps 2a and 2b

Step 4. Add the numbers in steps 1b, 2a, 2b, 3a, and 3b, and you get this:
9547 + 2 + 9999 + 9999 = 9549 + 20,000 - 2 = 29547, the number in the envelope.I'll let others weigh in for that one.

Thanks @Mark44. I have a clue for that the trick is in magical number 9999 if you have taken a 5 digit number in the envelop. And rest you can get from the number theory. And anyone can do this for any number range.