Is this solvable? Tks in advance!

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# Question

# Answer

I am not sure of the answer as think the question should have added more conditions or else there may have more than 1 solution.

The below solution is assuming that the question is asking for the MAXIMUM number of cuboids that can be added for the cuboids to be above the water surface.

Volume of a cuboid = 4 × 4 × 11.25 = 180 cm³

6 cuboids can be placed on same level of the tank, with 4 cuboids 4cm side fitted along side with the 18 cm length of the tank and 2 cuboids with 11.25cm side parallel with the 18 cm length of tank.

Height of water increase for each cuboid = 180/ (20 × 18) = 0.5 cm

Height of water increase for each layer of 6 cuboid placed = 6 × 180/ (20 × 18) = 3 cm

For each layer of 6 cuboids, the height of the cuboid 4cm is added.

For every 3 layers of 6 cuboids, 2 cuboids can be added in the remaining space with 11.25 side placed along side with height of the tank.

For every 3 layers of 6 cuboids and 2 cuboids, the height of the water added is 3 × 3 + 2 × 0.5 = 10

and there is a gap of 12 – 11.25 = 0.75 cm for the 2 additional cuboids every 3 layers which mean another 2 cuboids can be added for 12 layers of cuboids

There were 12/3 × ( 3 × 6+ 2) + 2 =82 cuboids for 12 layers of cuboids.

Original height of the water is 14 cm.

If 24 layers of cuboids were added, the height of the cuboids were 24× 4= 96 cm

Total number of 24 layers of cuboids were 82 × 2= 164

Height of the water = 14 + 164 × 0.5 =96 cm.

So in total the maximum number of cuboids required were 164 + 1 = 165 cuboids.

That will make the height of the cuboids to be 4 × 25 =100 cm and the height of the water 96.5 cm.

If there are no such restriction of maximum, the minimum cuboids required is 2 as stacking with 11.25cm side of cuboid along the height of the tank needed 2 cuboids to have height equal to 23cm well above the water height of 14 +1 = 15 cm.

However, there seems to be even more cuboids can be put into the tank if follow the above way with all cuboids put in the way that 11.25cm along side of the height of the tank.

20 cuboids can be put in one layer of cuboids with the height being 11.25cm.

If 10 layers of cuboids are put into the tank. Total cuboids are 10 × 20 = 200 cuboids.

Height of cuboids = 10 × 11.25 = 112.5cm

Height of the water = 14 + 200 × 0.5 = 114 cm

So the maximum number of cuboids are 201 cuboids with height 112.5 + 4 = 116.5 cm and height of the water 114.5cm.

Note: I had corrected my answers so many times and still thinking may be answer is wrong , this is really too difficult for psle!

I agree. It is a bad question. What about water displacement when the cuboids are placed in the water? That will increase the height of the water.