RE: Math mini-contest problem for Day 26 on D.Buzz for February 2021 😎

Answer for Day 26 Math Problem

  • 40 cubes 🎯

  • 42 cubes 🎯

  • 46 cubes 🎯

Any of the three answers shall be accepted, due to possible differing solvers' perspectives regarding the original problem. No solution required (but is recommended)!

Solutions

First, we should take note that we can look at the cake in 5 different positions (top, left, right, front, and back). Looking at either the left or right, or front and back, will give the same results.

If the solver assumes that the dimensions 6 by 8 by 5 (cubic units) are in the conventional xyz order and facing the xy plane, then there are 6 cubes horizontally, 5 cubes vertically, and 5 cubes forward. We will simply need to count all the cubes which have 2 or 3 sides with icing on the edges and corners.

This solution will assume that the cake is 6 cubes wide, 8 cubes high, and 5 cubes long.

  • For each layer at the bottom (1st) layer to the 7th layer, there are 4 qualifying cubes, which are at the edges. All of them have 2 sides with icing. There are a total of 28 qualifying cubes.
  • On the top (8th) layer, all the edges and corners qualify. There are 4 corner cubes (whose 3 sides have icing) and 14 edge cubes (whose 2 sides have icing), for a total of 18 cubes.

There are a total of 46 qualifying cubes using the conventional ordering of dimensions and plane of reference.

If you interchange the width (x) and the height (y) to 8 cubes wide and 6 cubes high (and length is still 5 cubes long), you will get the following:

  • For each layer at the 1st layer to the 5th layer, there are 4 qualifying cubes, which are at the edges. All of them have 2 sides with icing. There are a total of 20 qualifying cubes.
  • On the top (6th) layer, all the edges and corners qualify. There are 4 corner cubes (whose 3 sides have icing) and 18 edge cubes (whose 2 sides have icing), for a total of 22 cubes.

There are a total of 42 qualifying cubes when the width and height are interchanged.

If the height and length are interchanged (such that the dimensions are now 6 by 5 by 8 cubic units), we will get the following:

  • For each layer at the 1st layer to the 4th layer, there are 4 qualifying cubes, which are at the edges. All of them have 2 sides with icing. There are a total of 16 qualifying cubes.
  • On the top (5th) layer, all the edges and corners qualify. There are 4 corner cubes (whose 3 sides have icing) and 20 edge cubes (whose 2 sides have icing), for a total of 24 cubes.

There are a total of 40 qualifying cubes when the width and length are interchanged.

If the width and length are interchanged (such that the dimensions are now 5 by 8 by 6 cubic units), we will get 28 qualifying cubes from the first 7 layers and 18 from the top layer, giving a total of 46 qualifying cubes.

If the width becomes the height, the height becomes the length, and the length becomes the width (such that the dimensions are now 8 by 5 by 6 cubic units), we will get 16 qualifying cubes from the first 4 layers and 24 from the top layer, giving a total of 42 qualifying cubes.

Winner: @eturnerx-dbuzz 🏅

1 HIVE has been sent to @eturnerx-dbuzz's Hive account. 💰

Mentions: @jfang003, @holovision, @ahmadmanga (@ahmadmangazap), and @minus-pi 🤔
 

Please tell me if you think there is something wrong with these solutions. Thanks! 😅

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