Sent from my Samsung Omnia II GT-I8000
The first mistake I noticed is in the units.
Then I noticed the error in 640, before the words "check again!" got my attention.
On further reading and thinking...
The obvious thing about the unit is the wrong use of cm for volume.
There are more issues:
a) 1st line: There should be units on both LHS and RHS of an equation.
b) 2nd line: cm / cm, or cm^3 / cm^3 gives unitless, not cuts.
c) 2nd line: this calculation should gives number of cubes, not number of cuts.
d) 2nd line: the idea behind this calculation may be workable only if they melt the block of cheese and re-mold it into a rectangular block with dimensions as multiples of the side of the cubes.
e) Are "2cm cubes" cubes of 2cm^3 or cubes of sides 2cm? Should be the latter.
f) Assuming that Mr. Muthusamy is skillful enough to keep the cheese nicely aligned together while making the following cuts:
- 5 cuts perpendicular to the 12 cm side to give 6 2 cm thick slices
- 4 cuts perpendicular to the 9 cm side to give 4x6=24 strips with cross-sectional area of 2x2 cm^2, and 4 strips with cross-sectional area of 2x1 cm^2
- 7 cuts perpendicular to the 15 cm side to give 7x4x6=168 2 cm cubes and 7x4 2x1x1 rectangular blocks.
Thus, in this way, the number of cuts is 5+4+7 = 16 cuts to get 168 2cm cubes. Is 16 the minimum number of cuts, and 168 the maximum number of cubes? It is not shown here, and I doubt it is expected in this question. However, if the answer is presented by drawings, then it may be obvious that this is the minimum number of cuts.