Easy but tricky
You have to choose a number from 1 to 9. Now add 4 to it. Multiply it by 3. Subtract 2. Now multiply it by 9 and add both of its digits together. Here is a sample you can refer to :
Chosen digit:1
1 + 4 = 5
5 x 3 = 15
15 - 2 = 13
13 x 9 = 117
Sum of digits = 1 + 1 + 7 = 9
Now do the same with your chosen digit. Is your final answer the same for everyone?
Note: Calculate the sum of the digits of the final answer until it gives a single digit number.
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4 solutions
@Kumudesh Ghosh , look at my proof and see where you went wrong.
I think you forgot to read the note given at the end of the question. ;)
Hlo, the number divisible by 9 has lastly came 9 on adding ....not a hard one...but not a bad one
Well,we are multiplying by 9.so,it has to be 9 or 0 in the end.Easy to see that 0 can't happen.Hence,9 always.
And if you sum the digits until getting a one digit number this works for all natural numbers.
A proof:
1 + 4 = 5 , 5 ∗ 3 = 1 5 , 1 5 − 2 = 1 3 , 1 3 ∗ 9 = 1 1 7 , S d = 9 , 1 + 1 + 7 = 9
2 + 4 = 6 , 6 ∗ 3 = 1 8 , 1 8 − 2 = 1 6 , 1 6 ∗ 9 = 1 4 4 , S d = 9 , 1 + 4 + 4 = 9
3 + 4 = 7 , 7 ∗ 3 = 2 1 , 2 1 − 2 = 1 9 , 1 9 ∗ 9 = 1 7 1 , S d = 9 , 1 + 7 + 1 = 9
4 + 4 = 8 , 8 ∗ 3 = 2 4 , 2 4 − 2 = 2 2 , 2 2 ∗ 9 = 1 9 8 , S d = 1 8 , 1 + 9 + 8 = 1 8
5 + 4 = 9 , 9 ∗ 3 = 2 7 , 2 7 − 2 = 2 5 , 2 5 ∗ 9 = 2 2 5 , S d = 9 , 2 + 2 + 5 = 9
6 + 4 = 1 0 , 1 0 ∗ 3 = 3 0 , 3 0 − 2 = 2 8 , 2 8 ∗ 9 = 2 5 2 , S d = 9 , 2 + 5 + 2 = 9
7 + 4 = 1 1 , 1 1 ∗ 3 = 3 3 , 3 3 − 2 = 3 1 , 3 1 ∗ 9 = 2 7 9 , S d = 1 8 , 2 + 7 + 9 = 1 8
8 + 4 = 1 2 , 1 2 ∗ 3 = 3 6 , 3 6 − 2 = 3 4 , 3 4 ∗ 9 = 3 0 6 , S d = 9 , 3 + 0 + 6 = 9
9 + 4 = 1 3 , 1 3 ∗ 3 = 3 9 , 3 9 − 2 = 3 7 , 3 7 ∗ 9 = 3 3 3 , S d = 9 , 3 + 3 + 3 = 9
Therefore, the answer is No as two out of the nine answer's S d 's = 18.
Therefore, @Kumudesh Ghosh , your answer is wrong.
S d = Sum of digits at end of working out.
Umm actually if you read the note given in The question you will understand that my answer is actually correct. But well spotted though!
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I think you can say "Calculate the sum of the digit again until it gives a single digit number."
The trick is in the last operation where you multiply the number by 9. It is known that the sum of digits of any multiple of 9 is 9 so it is clear that everyone will receive the same answer, regardless of their previous choices or operations. Hope you liked the question.