Hello all. Welcome to the 9th of our Gifted World challenge series. Below the question, you will also find __the solution and featured responses__ we received for __Challenge number 8__.

This week's challenge is to check the reasoning of a popular WhatsApp forward. Give it your best shot!

## Challenge #9

**Post your answer here - **__https://forms.gle/qfsp4846NZdZwoKb8__

Critically analyse this WhatsApp forward -

This is the CCTV footage from a lift in a high rise building

A man took the battery of an e-bike into the lift. As soon as the lift's doors closed, the battery first caught fire and then immediately exploded. Maybe the electro-charge in the battery exuded a strong magnetic field which was too much for the confined metallic cabin of the lift.

Kindly send this video to your near and dear ones, and please do not carry a high power rechargeable battery inside a lift.

__For this challenge. analyse which parts of this explanation are believable and possible, and which parts are not. For aspects that you don't think are accurate, can you provide an alternative explanation that describs why that happened.__

**Post your answer here - **__https://forms.gle/qfsp4846NZdZwoKb8__

Last day to submit answers is Saturday, August 10. The 3 best answers (as judged by the Gifted World team) will be featured on our blog. We don't have a particular 'right answer' in mind, so give it your best shot! Looking forward to some creative submissions.

This challenge has been given by Karthik Raghavan and Siddharth Bharath. If you enjoyed it, do check out the masterclass by Karthik Raghavan coming up in August - __The Magic of Distance__

## Solution to Challenge #8

__Challenge number 8__ involved finding out how to split the electricity costs of an elevator among the different floors of an apartment building. We received 10 responses to the questions. We present the three best answers below

### Split the cost based on distance travelled

This solution was given by __Sahana Ravikumar, Grade 10, The Deens Academy, Whitefield, Bangalore__

```
"Let cost for first floor be x, 2nd 2x and so on
x+2x+3x...+12x=6000
78x=6000
```

```
x is approximately 77
Justification -
The lift covers double the distance to go the second floor from ground than it does to go to the first floor from ground so by logic, the cost should also be a double. We can repeat this similar pattern and derive the equation above.
Bonus: there shouldn't be any change in the split up because the person living on the 12th floor could also argue that they are using the lift simultaneously with another person uptil the 11 th floor and thus they aren't causing any additional usage until they are moving from the 11th floor to the 12th floor. The split up should be the same as the one I have mentioned above. "
```

Other students who arrived at a similar solution were -

Samuel D'Costa Grade 8 Pearl Wisdom School, Dubai

### Charge all floors equally

This solution was given by Anshuman Tripathy, Grade 9, Delhi Private School Sharjah

```
"At first, it seems like the lawyer, who is on the first floor, should not pay the same amount as the person living on the top floor who goes up and down 12 floors each time. Definitely, the 12th floor resident should pay more.
But then, when we think about it, we realize that splitting the costs equally is actually beneficial. Sure, the lawyer lives on the first floor. but she is the one who has the accessibility and convenience of using the lift. She can easily use the lift up and down and doesnâ€™t have to spend time waiting for others to get out of the lift compared to the person on the 12th floor when the lift is full. She, therefore, gets an added advantage. The aforementioned ultimately prove that the lawyer is the one who actually should pay higher.
however, keep in mind that whenever there is inequality or if someone pays more than others for the same thing, it can create an unhealthy ecosystem in the building. People paying more than others for the same thing will always taunt those paying less, which will not be good for the building community. But when all the people pay the same price, it will build relations between the residents and create a great ecosystem within the building."
```

```
My justification for the lawyer to keep on paying equal amount and why paying equal amount is the best:-
1)Accessibility and convenience - Residents living on lower floors like the lawyer have an added benefit of not waiting for other residents to come in or getting out and thus can easily travel through the lift. They are the ones who can also use it much more quicker than others and thus provides them with another benefit.
2)Fairness in community - when people pay the same amount, it helps make the ecosystem in the building community much more better and helps people bond.
3)Simplicity - The billing system will be much more efficient and easy to calculate when all the people pay the same equal amount rather than equating every individual's amount.
4)A healthy ecosystem - As mentioned earlier, it will help in making the community and relations between residents much better considering each and every resident pays equal amount.
Therefore,in conclusion, splitting the electricity bill for the lift equally among all 12 residents is justified and beneficial. Each resident pays rupees 500 per month, accepting both the equal accessibility and the convenience factors. This ensures fairness, simplicity, and a harmonious community within the building."
```

Other students who arrived at a similar solution were -

Viraj Singh, Grade 6, The Indian High School, Secondary Campus, Dubai

### Base price + weighted usage charge

This solution was proposed by Vihaan Harrison, Grade 8, Delhi Private School Sharjah

`Step 1: Base Charge: Keep a base charge that can be a flat amount, say `INR 100`, or a small percentage of the total bill, say 10%, to account for the scenarios wherein the lawyer benefits from a shared elevator ride; this would be the case of minor impact on electricity consumption when the elevator is already in use.`

`Step 2: Weighted Floor Usage Factor: Each floor will weigh depending on the distance from the ground floor. This weight could be the floor number, or you can introduce a progressive weighting system which increases the weight more significantly at higher floors. For example, weights of 1, 2, 3, 4, 5, 7, 10, 13, 16, 20, 25, and 30 where the gap between weights increases as the floor goes up. This stronger weighting penalises higher floors more for their greater lift usage.`

`Step 3: Calculate Floor Contribution: Take the residual amount of the electricity bill, that is, the total bill minus the base charge, and divide it by the sum of all the weighted floor usage factors, that is, the weight of floor 1 plus the weight of floor 2 plus. Plus the weight of floor 12. This will yield the cost per weighted usage factor.`

`Step 4: Multiply by Weighted Usage Factor: Multiply the cost per usage factor by the weighted usage factor for each floor. This gives you the incremental contribution for each floor by distance travelled.`

`Add up Charges: Add the base charge you developed in Step 1 with the incremental contribution computed in Step 4. This becomes the monthly contribution for each floor." "The base charge means that everyone pays at least something, recognizing the fact that everybody benefits from a running lift.`

`The weighted floor usage factor means higher floors pay more due to their greater liftings. The weighting allows one to shift the penalty as desired for higher floors.`

```
Benefits:
More fair than equal split: Takes into account use by floor
Recognises shared rides: Base charge stops lawyer being penalised for just gaining the benefit of an already running lift.
Flexibility: The weighing system to be used can be adapted based on the preferences of the residents.
```

```
Implementation:
Inside the building, negotiate and agree with all residents on a base amount and a weighting system. Provide a table indicating the weights per floor, detailed calculations, and the final monthly contribution each floor has to pay. This combined solution is fair and adaptable to splitting an electricity bill by considering individual usage and further shared lift rides."
```

Thank you all for your enthusiastic participation. Looking forward to keep engaging with you all.

## Comments