Puzzle of the Week
We have some numbers written in a row. We want to place + and – signs between them so that we get a 0.
For example,
If we place the signs in between them as shown below, we get a 0.
Can you find a way to place the signs between 1 to 10 so that you get a 0?
What students worked out22
Student 9
sir can we repeat the numbers ?
Student 2
I don’t think that we can repeat numbers
Karanteacher
No, We can’t repeat numbers in this version. Maybe, you can explore what happens if we are allowed to repeat numbers.
Student 9
sir can we repeat the numbers
Student 9
if yes then
1+2-3+4+5-6+7-8+9-10-1=0Student 9
if yes then 1+2-3+4+5-6+7-8+9-10-1=0
Student 2
sir, I claim that without repeating it is not possible as I discovered that in 1,2,3 it is possible as 1+2+3==even number if it is equal to an odd number you can’t get “0” 🙂 🙂 🙂 🙂 🙂 🙂 🙂 🙂
Student 11
Sir I also think it is impossible
Student 11
2 ways If we are allowed to repeat 1 number only once
1) 1-1-2+3-4-5+6-7+8-9+10
2) 1+2-3+4+5-6+7-8+9-10-1Karanteacher
So, we see some possibilities if we are allowed to repeat. Why do you think it’s not possible without repeating?
Student 11
1 more
1+2+3+4-5+6+7+8-9-10-5Student 2
if we could repeat then there are a lot of possibilities
Karanteacher
That’s true!
Student 2
and it will be very simple which won’t be a challenge 🙁
Student 1
I think it is impossible without repeating
Karanteacher
Why do you think so?
Student 1
Can we use negative numbers
Student 1
We can not make 0 because the sum of the numbers of 1-10=odd number
Student 4
Are we allowed to rearrange the numbers🤔?
Student 9
Yes sir. I think it is impossible without repeating the numbers.
Student 9
sir if we are allowed to rearrange the numbers then we can do this;-10×2-9-5+6-8+1+4-7
Student 3
total of all numbers is 55 which is odd
so its not possible to get 0