Just a guess . . . 1,024
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To cut a cube into 504 identical pieces, you would need to make 503 cuts. Each cut divides the cube into two pieces, so the first cut creates 2 pieces, the second cut creates 4 pieces, the third cut creates 8 pieces, and so on. Therefore, to reach 504 pieces, you would need to make 503 cuts.
I think you can make 12 pieces at most
Cut a pizza into 2 using one straight cut. Stack the pieces and make a straight cut: you now have 22 = 4 pieces from 2 cuts. Stack these and make a straight cut: you now have 23 = 8 pieces from 3 cuts. Continue. After 7 cuts you can have 27 = 128 pieces. You can reduce the number of pieces to 29 if, after the fourth cut, you stack and cut only 11 pieces and thereafter cut just one each time. There are other options which give the same result.
If you want an even-sized pieces, you can make a 7-slice pizza. Otherwise, the maximum is 22. (.5x^2 + .5x + 1 is the formula to determine the maximum number of slices if you use "x" cuts.) If you want even-sized slices, you can make a 7-slice pizza. Otherwise, the maximum number of slices is 22. (.5x^2 + .5x + 1 is the formula to determine the maximum number of slices if you use "x" cuts.)
A log would need three cuts to make four pieces. Here are 4 pieces. The "." represents each of the cuts. =.=.=.= So, 3 cuts at 3.20 per cut is 9.60 3 x 3.20 = 9.60