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Challenge 1
We were sent correct solutions to the this challenge by Dhruv and by Viha, Abhiram, Eshann, Anirved, Arya, Rivaan, Miraya, Asma, Aprameya, Vibha, Rudraraj, Nithyashree, Adhrit, Kathir and Arnav from Ganit Kreeda, Vicharvatika. Thank you all for sharing your ideas with us. Here is Asma's solution, which can be clicked on to make it bigger:
Well done to all of you for working that out!
Challenge 2
We haven't yet received any solutions for the second challenge. Rivaan came up with this formula, which he used algebra to simplify:
Paint required for cubes = Paint required for outside of box
6(l-2)(w-2)(h-1) = 2(l×h)+2(w×h)+2l+2(w-2)
6lhw-6lw+24h = 14lh+14wh-10l-10w+20
The children from Ganit Kreeda then tried to solve this formula using various methods, but couldn't find a solution. This formula is correct, but I wonder if there are any different ways you could approach this challenge?
Challenge 3
The children from Ganit Kreeda used trial and improvement to find this solution:
Box dimensions | Number of cubes | Paint for cubes | Paint for box |
4×4×2 | 4 | 24 | 44 |
Anirved found this solution to Challenge 3, which can be made bigger by clicking on it:
Well done to all of you for finding those. There are a few more possible solutions - please do email us if you think you've found them.