DIY Challenge 1: Always the same answer

Imagine you are performing this trick with your friend.

Can you always guess the final answer? Try it with a few different starting numbers.

What do you think is the trick here?

What students worked out19

Student 22020-11-23
the end answer is always 2
THE TRICK HERE IS THAT:
when we multiply the next number will be a multiple of 3 as it is going X3 and after that -3 it will still stay a multiple of 3 then divided by 3 the number will be more 2 more than the other number, therefore, resulting in the answer 2 🙂
- Student 22020-11-23
  :):):):):):):):):):):):):):):):):):):):):):):):):):):):)
  :):)if my answer is not clear I can explain in class:):)
  :):):):):):):):):):):):):):):):):):):):):):):):):):):):)
  - Karanteacher2020-11-24
    What do you think happens if we replace the 3 by 5 in each of the steps?
    - Student 22020-11-24
      IF IT IS 5 THE END NO WILL BE 4 MY PREDICTION THIS IS BEFORE I HAVE TRIED
      1=0
      2=1
      3=2
      4=3
      5=4
      6=5
      7=6
      8=7
      9=8
      AND SO ON
      OBSERVATION
      THE NUMBER IS ONE LESS THAN THE NUMBER WE ARE USING THE REASON IS THAT
      EXAMPLE IF WE ARE USING NUMBER 3:
      
      when we multiply the next number will be a multiple of 3 as it is going X3 and after that -3 it will still stay a multiple of 3 then divided by 3 the number will be more 2 more than the other number, therefore, resulting in the answer 2
Student 112020-11-23
It is always 2
- Karanteacher2020-11-23
  Why do you think it’s always 2?
Student 12020-11-23
Its always 2
- Karanteacher2020-11-24
  Can you explain the reason?
- Student 12020-11-24
  when we add and multiply then divide and sub we end up with a number that is =2 when we sub the number also a multiple of 9 except 1.
Student 112020-11-24
If we replace 3 by 5
1-5
2-6
3-7
4-8
5-9
6-10
7-11
8-12
9-13
Like that it will increase one.
- Student 32020-11-29
  i totally agree with this answer
Student 112020-11-24
I can’t find the reason
Student 22020-11-24
ANSWER TO SIR’S QUESTION
IF IT IS 5 THE END NO WILL BE 4 MY PREDICTION THIS IS BEFORE I HAVE TRIED
1=0
2=1
3=2
4=3
5=4
6=5
7=6
8=7
9=8
AND SO ON
OBSERVATION
THE NUMBER IS ONE LESS THAN THE NUMBER WE ARE USING THE REASON IS THAT
EXAMPLE IF WE ARE USING NUMBER 3:

when we multiply the next number will be a multiple of 3 as it is going X3 and after that -3 it will still stay a multiple of 3 then divided by 3 the number will be more 2 more than the other number, therefore, resulting in the answer 2
Student 142020-11-26
When you complete step 5, you get a number 2 times more than the number which you started with.
Student 42020-11-27
The last number is always 2
Student 42020-11-27
I think it is because whenever we take a no. and + x,× by x,- x. and ÷ by x,the answer is always the number we started with + 2
e.g. if we take 7,add 3,multiply by 3, subtract 3 and divide by 3, the answer is 9. And then if we subtract 7, the answer is 2, which is 3-1
Student 122020-11-28
yes sir always 2
Student 152020-11-29
ya sir its always coming out to be 2
Student 92020-11-29
I think it ends at 2 because whenever add, multiply, subtract and then divide it by 3 and subtract it by the number which you started with the answer is always 2.