Math Is Fun Forum

AtotehZ

Novice

Registered: 2025-03-04

Posts: 2

Geometry problem

Hello, this is my first post here.

I'm looking for help for a geometry problem.

Multiple shapes has to be placed as close to another shape on a grid as possible.

The different shapes are:

2x2 squares(A). There are 100 of these and they have to be placed as close to another shape I'll mention below as possible.

3x3 square(B). There are 2 of these. There can be no more than 7 tiles between the 2 B's. The primary goal is to place the 100 A's as close to one of the B's as possible.

The last shape complicates it a bit.

1x1 square(C). This shape creates a 7x7 area(D) underneath it(C always in its center) and all A's must have all 4 tiles placed on top of the area it creates, however not on C itself.

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So to solve the problem:

All 100 A's must be as close to the 2 B's as possible while also being on top of D areas. Placing the C's without obstructing too much is key.

Below is an incomplete attempt:

Bob

Administrator

Registered: 2010-06-20

Posts: 10,702

Re: Geometry problem

hi AtotehZ

Welcome to the forum.

I'm not yet fully understanding the problem.

I'm not seeing area D at all. Would you show, on a new picture, a D area alongside the other squares?

Are shapes allowed to overlap?

Are 'holes' allowed where the grid shows through with no squares?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

AtotehZ

Novice

Registered: 2025-03-04

Posts: 2

Re: Geometry problem

Sorry for the late reply, I subscribed to get answers via mail, but didn't see any.

Area D is the only one allowed to overlap. A, B and C are not. In fact A *has* to overlap fully with D.

Area D is as described in the problem, it is not seen in the visual representation. I can upload an amended version that shows the figures more clearly.

I've added shape letters to all except A's.

I have outlined the D area around one of the C's. I have not done so with all as it'd become confusing without some sort of interactivity to enable and disable it.

I have also added E's. The E's are essentially inefficiencies. It'll never be perfect with the restrictions that exist.

I hope this answers the questions you had.

Thank you for the welcome to the forum.