# Treasure Hunt from Outside the Grid

The applet below presents a modification of a puzzle invented by the late math educator and researcher Tom O'Brien, also known under the nom de plume of Professor Tobbs. The game is to teach elementary school students logical thinking. The goal of the game is to find a treasure hidden under one of the squares in a 4×4 grid. The way to locate the treasure is by touching a square on the grid. If you are lucky to stumble on the square that conceals the treasure the game stops. Otherwise, you are given a clue - the taxicab distance from the selected square to the treasure. You may touch as many squares as you need to solve the puzzle.

In the modified version you touch the regions outside the grid, one step away so to speak. I believe this modification is more suggestive of why touching a corner square reveals a diagonal that contains the treasure, although the reason is pretty simple anyway.

What if applet does not run? |

### Taxicab/City-block Distance.

- Treasure Hunt in a Square Grid
- Treasure Hunt from Outside the Grid
- Objects distant and near
- Farmer and Wife To Catch Rooster and Hen
- Distance Formula
- What Is Geometry?

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Copyright © 1996-2018 Alexander Bogomolny

Why touching a corner square reveals a diagonal that contains the treasure.

For the taxicab distance, the cells equidistant from a given one form a square that rests on one of its vertices, like a common depiction of a rhombus. The sides of that square are inclined 45° to the grid lines. The vertical line through the center is a diagonal that passes through two vertices. A similar remark applies to the horizontal line through the center and the other two vertices. It follows that when the center of the rhombus is located at the corner of the grid the vertices of the rhombus fall into the extreme squares of the grid with only room to a single diagonal between them.

|Contact| |Front page| |Contents| |Arithmetic| |Eye opener|

Copyright © 1996-2018 Alexander Bogomolny

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