What is the big idea behind Tanks?

An advanced Tanks puzzle. Image by BrainQuake

Each of the three puzzles in the new BrainQuake app has some mathematical features different from the others, reflecting the different ways mathematics is used in the world.

The Gears puzzle is all about optimization, almost certainly the single most common use of mathematics in today’s world. Gears is not about finding a unique answer (many important real-world problems do not have a unique correct solution), rather finding better answers or an optimal answer. Tiles is about finding an answer when there are several–or maybe many–correct answers. (Also common in real world applications of mathematics.) And Tanks puzzles all have unique correct answers. (Yes, the real world keeps presenting problems of this kind as well.)

Those are not the only distinctions, though. Another is that, although all three puzzles break the Symbol Barrier, they do so in ways that differ in some regards.

Gears does so in a deep way that presents mathematics usually regarded as high-school or college level in a manner that is accessible to a middle schooler. On the face of it, Gears (the puzzle that constituted our launch app Wuzzit Trouble) is an (elementary) arithmetic app, but in point of fact the mathematics it involved is (advanced) algebra.

Tiles looks like a spatial reasoning app but in addition to spatial reasoning it presents problems involving linear functions and growth. The earlier posts about Gears and Tiles in this blog, linked above, provide illustrations to show how the puzzles encode the mathematics.

With Tanks, however, it’s almost a case of “what you see is what you get.” It’s self-evidently about ratios, proportions, and fractions. It breaks the symbol barrier and achieves much of its learning power in an explicit and easily recognizable manner, by providing a mechanism to explore those concepts.

[I said “almost” just there because more advanced puzzles require much more than mastery of basic fractional arithmetic. As with all our puzzles, the ultimate focus is on number sense, mathematical thinking skills, and creative problem solving capacity. See how you do when you move up the levels in the Tanks puzzle. If you are like others who have played Tanks, you are likely to find yourself saying, “This one cannot be solved. There must be a bug.” Well, we’ve tested the puzzles a lot. While we cannot say with 100% certainty there is not a bug we’ve missed–this is software after all–it is pretty unlikely. Much more probably, you need to keep trying to find a solution.]

Since Tanks “wears its mathematics on its sleeve,” rather than throw more words at you, let me show you some of the more basic Tanks puzzles in action. They are all super-short videos. (These all have two output tanks. More advanced puzzles have three or four output tanks––though higher level puzzles with just two tanks can be fiendishly difficult.)

A Tanks puzzle with a percentage wheel valve. (Slight delays are my thinking time.)
A Tanks puzzle with an area wheel valve
This one requires three transmissions to fill the output tanks
A Tanks puzzle with a fraction wheel valve
A Tanks puzzle with a radial valve with fraction labels
A Tanks puzzle with a circular valve labeled with decimals in the unit interval
Two Tanks puzzles with rectangular valves labeled by decimals in the unit interval

You’ll find lots more where those come from on the BrainQuake app.

More advanced Tanks puzzles require several successive valve settings to complete the puzzle, providing multi-step mathematical thinking challenges like the ones in advanced Gears puzzles

– Keith

Developing children’s true math proficiency