Where is the answer key?

On the second page of every puzzle. There is no separate key to download: generate a puzzle and it prints as two pages, the puzzle and then its worked answer.

Can the printed answer ever be wrong?

No. The answer is taken from the same figure the puzzle was drawn from rather than solved again, and every figure is checked before it prints, so the answer always matches the puzzle.

Are these spatial reasoning puzzles with answers free to print?

Yes. Generate the puzzle above and print it with its answer, at no cost and with no sign-up. It is free for classroom, home and personal use.

Do the spatial reasoning puzzles with answers come with answers?

Yes. Every puzzle prints as two pages: the puzzle on page one and the total cube count on page two. The answer is drawn from the same figure as the puzzle, and every figure is checked before it prints, so the answer is never wrong.

Can I make a spatial puzzle book to sell on KDP?

Yes. The free tool makes one puzzle. Publisher Studio generates hundreds of graded puzzles of one type, with an optional how-to-solve page, at any KDP trim, as a print-ready 300 DPI interior and answer-key PDF, so you can publish a book.

Free printable

Spatial reasoning puzzles with answers

Every puzzle here prints with its answer on the second page: the cube total, the three filled-in views, or the finished solid. Answers come from the same figure the puzzle was drawn from, so they are never wrong. Generate a puzzle, print both pages, and mark it yourself.

Puzzle type

How many cubes make up the stack, including the hidden ones?

Difficulty

Shape

One dense solid stack.

Two pages: the puzzle and its answer. Every figure is checked before it prints, so the answer is never wrong, by the same engine as our KDP studio.

Want the whole book?

This makes one puzzle. Sign up to turn this puzzle type into a full 3D spatial book for Amazon KDP: hundreds of puzzles at any trim, as print-ready PDFs. We carry your puzzle type and difficulty into the studio.

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Preview

The puzzle and its answer, as they print.

Puzzle Medium

How many cubes make up this figure — including the ones you cannot see?

1
Puzzle Medium · Answer

25 cubes

2

Every puzzle prints its own answer

There is no separate answer key to find or buy. Each puzzle prints as two pages, the puzzle first and the answer second, whichever type and grade you choose. For cube counting the answer is the total; for draw the views it is the three grids shaded in; for build the solid it is the finished shape drawn on the isometric grid.

The answer is read from the exact figure the puzzle was drawn from, not solved a second time, so it cannot disagree with the puzzle. Every figure is also checked before it prints, which for build the solid means exactly one shape fits the three views.

Why a checked answer matters

A worked answer turns a puzzle into something a child can do alone and a teacher can set for a whole class. Nobody has to adjudicate a disagreement, and a parent helping at the kitchen table does not have to solve a hard stack themselves to know whether the answer is right. Print the puzzle, keep the answer page aside, and bring it out to mark.

3D to a number

Count the cubes

A stack of unit cubes drawn in 3D on a faint floor grid, and one question: how many cubes make up the figure, including the ones you cannot see?

How to solve it

1Count what you can see, from the bottom up. Work one layer at a time. Count the cubes in the base, then the next layer, and so on to the top.
2Add the hidden cubes. A cube sitting high up must have cubes underneath holding it up. Those supporting cubes count too, even when you cannot see them.
3Check the base is solid. Wherever a tall stack stands, every cube below it is there. Add those in and you have the total.

The one rule that makes it solvable: Every cube rests on another, so nothing floats in the air, and the whole figure is one connected piece. That is how you know a hidden cube is really there.
What the answer page shows: The answer page repeats the figure with the total printed beneath it.
How the grades differ: Easy is a 3 by 3 by 3 stack of 4 to 14 cubes. Medium is 4 by 4 by 4 with up to 26. Hard is 8 by 8 by 8 with up to 130 cubes and at least 40 hidden. Expert is 12 by 12 by 12 with up to 260 cubes and at least 70 hidden.
Good for: A first spatial puzzle for children, reasoning-test practice, and adult solvers at the hard and expert grades.

The other two puzzle types

Making a whole puzzle book?

This page makes one puzzle. To publish a book on Amazon KDP, the KDP spatial puzzle maker generates hundreds of graded puzzles at any trim, as a print-ready 300 DPI interior and answer-key PDF. Generate once, export unlimited sizes.

More printable spatial puzzles

See every printable spatial puzzle

Questions

Where is the answer key?: On the second page of every puzzle. There is no separate key to download: generate a puzzle and it prints as two pages, the puzzle and then its worked answer.
Can the printed answer ever be wrong?: No. The answer is taken from the same figure the puzzle was drawn from rather than solved again, and every figure is checked before it prints, so the answer always matches the puzzle.
Are these spatial reasoning puzzles with answers free to print?: Yes. Generate the puzzle above and print it with its answer, at no cost and with no sign-up. It is free for classroom, home and personal use.
Do the spatial reasoning puzzles with answers come with answers?: Yes. Every puzzle prints as two pages: the puzzle on page one and the total cube count on page two. The answer is drawn from the same figure as the puzzle, and every figure is checked before it prints, so the answer is never wrong.
Can I make a spatial puzzle book to sell on KDP?: Yes. The free tool makes one puzzle. Publisher Studio generates hundreds of graded puzzles of one type, with an optional how-to-solve page, at any KDP trim, as a print-ready 300 DPI interior and answer-key PDF, so you can publish a book.

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