Perspective – 3D cube puzzle from views

How it works

The thinking is spatial, the controls are flat: a cube body has three dimensions, each view only two — and what is lost in between is the puzzle. You build on a grid of 3×3 squares. Each square carries a stack of 0 to 3 cubes: a tap raises the square by one and wraps from 3 back to 0. Next to the grid you see your body as a drawing, along with the number of cubes you have used so far.

The task consists of up to three pictures:

• COLUMNS shows the tallest stack in each column.
• ROWS shows the tallest stack in each row.
• SQUARES shows which squares are filled at all and which stay empty.

So the bars show only the tallest stack — anything lower behind it disappears. That is why several bodies fit the same pictures. You are not looking for just any of them but for the smallest: the one with the fewest cubes. Every puzzle has exactly one such body.

“Check” submits your body. Afterwards each view is marked as fitting or not fitting — and that is all; individual squares are never highlighted.

On this page Perspective starts in practice mode: the puzzle type is already selected, so you choose Easy, Medium or Hard and begin. As often as you like, nothing is scored, and the clock counts upwards rather than being a budget. The cube puzzle can also be picked as the puzzle type of a duel; it does not appear in the Daily Sprint, in Endless or in Deduction Rush.

Tips & techniques

• Every square has a ceiling. A stack may not rise above the bar of its column, nor above the bar of its row. So a square can never be taller than the smaller of the two — and a square that SQUARES shows as empty stays empty.
• Every bar needs a carrier. If a column shows height 3, at least one square in that column must be exactly 3 tall. The same goes for every row. For each bar, ask yourself: which square can carry it at all?
• One stack can carry two bars at once. When a column and a row have the same value, a single stack where they cross covers both. This is where the savings are — look for such crossings first.
• All the way down or all the way up. In the smallest body every square is either as low as it can be — one cube if it has to be filled, none otherwise — or exactly at its ceiling. A value in between carries no bar and still costs cubes.
• Do not raise everything the pictures allow. Filling every available square as high as the pictures permit fits the pictures and is still never the solution. For each tall stack you should be able to say which bar it carries that no other stack does.
• Keep an eye on the cube count. Your own count is shown next to the drawing. The count you are aiming for is shown nowhere — it is the question.
• Look behind the question mark. A small figure there shows two different bodies with the same pictures: one made of four cubes, one of eight.

Frequently asked questions

What kind of game is this?

A 3D cube puzzle: instead of a grid of digits you fill a 3×3 grid with stacks of 0 to 3 cubes, and the task is given as flat views of a body. No dexterity is needed: there is nothing to hit and nothing to time, only something to work out. More views would add nothing, by the way — the back view is the mirrored front view, and the right one the mirrored left.

Am I supposed to rebuild the body from the pictures?

Not quite — and this is the most common misunderstanding. The pictures do not pin down one particular body, because they show only the tallest stack per column and row. You build the most economical body that fits all of them.

Every view fits, but it does not count as solved. Why?

Your body matches the pictures but uses more cubes than necessary. Look for stacks that are not the only carrier of any bar, and lower them.

How do the difficulty levels differ?

The grid stays 3×3 with heights from 0 to 3 at every level. On Easy and Medium all three pictures are given; Medium has more squares where the obvious move of raising them would be wrong. On Hard the SQUARES picture is missing — there you also have to work out which squares are filled at all, and fill as few as possible.

Are there hints, or a solution I can look at?

Perspective has no hints: the answer emerges as a whole, and naming a single square would mean giving away a piece of the solution. Instead, after an attempt in which every view fits, you can have the solution shown. The smallest body then appears beside your own, so you can compare square by square. The puzzle then counts as skipped, not as solved.

Do I have to guess?

No. The smallest body is unique in every puzzle and can be worked out from the pictures. In practice mode a failed attempt costs nothing.

Does it cost anything, and do I need an account?

No and no. Perspective runs free of charge in your browser, and you can play at once without signing up.