Help With These Math Problems!

<p>Can anyone explain to me how to solve these two grid-in problems?</p>

<ol>
<li>The sum of the positive odd integers less than 100 is
subtracted from the sum of the positive even integers
less than or equal to 100. What is the resulting
difference?</li>
</ol>

<p>2.A large solid cube is assembled by gluing together
identical unpainted small cubic blocks. All six faces
of the large cube are then painted red. If exactly 27 of
the small cubic blocks that make up the large cube have
no red paint on them, how many small cubic blocks
make up the large cube?</p>

<p>For the first problem, instead of going to 100, try going to 10 and multiply that by 10 (10 x 10 = 100)</p>

<p>To 10:
Odd numbers summed up: 1 + 3 + 5 + 7 + 9 = 25
Even numbers summed up: 2 + 4 + 6 + 8 + 10 = 30
Even - Odd = 5</p>

<p>So the diffrence is 5 for a set of 10, and a set of 100 is 10 x 10 , so the diffrence is 5 x 10 or 50.</p>

<p>2.A large solid cube is assembled by gluing together
identical unpainted small cubic blocks. All six faces
of the large cube are then painted red. If exactly 27 of
the small cubic blocks that make up the large cube have
no red paint on them, how many small cubic blocks
make up the large cube? </p>

<p>27 have no paint, meaning they are the core and don’t show on the surface. cube root 27 gives you 3. so the core cube is 3x3x3.</p>

<p>Add to that top and bottom surface which are 4x4 each. (32 + 27 = 59)
Then add 2 sides opposite each other while not counting the ones that overlap into the “top” and “bottom” they are 2x4 each. (16+59 =75)</p>

<p>Then add last remaining sides without using overlapping cubes so they are 2x2 each. (8 + 75 = 83)</p>

<p>83 cubes.</p>

<p>I think I may not have explained enough, but I hope I did ok. Hopefully no math errors either.</p>

<p>@etotheitimespi: thanks for the help. yes the ans is 50 and its clear to me now.</p>

<p>@Kalookakoo: the correct ans given is 125, not 83 :frowning: Its possible that there is a mistake somewhere</p>

<p>The inner cube is a 3x3x3. The larger cube is a 5x5x5.</p>

<p>thanks xiggi, but could you please clarify? why it should be 5^3 ?</p>

<p>All sides of the 3x3x3 have to be covered with a layer of additional blocks.</p>

<p>thanks xiggi :)</p>