--- title: "Hard cube counting puzzles: free printable with answers" description: "Free printable hard cube counting puzzles with answers. Big stacks of up to 130 cubes with at least 40 hidden. No sign-up." source: "https://www.oncebooks.com/spatial-puzzles/hard" --- 1. [Home](https://www.oncebooks.com/) 2. [Spatial puzzles](https://www.oncebooks.com/spatial-puzzles) 3. Hard Free printable # Hard cube counting puzzles Hard cube counting puzzles use an 8 by 8 by 8 stack of up to 130 cubes, and at least 40 of them are hidden behind or beneath the others. You cannot count what you see and stop there. Work the footprint, then the heights, and reason about the volume. The full answer prints on page two. PuzzleDesign Puzzle type Count the cubesDraw the viewsBuild the solid How many cubes make up the stack, including the hidden ones? Difficulty EasyMediumHardExpert Shape BlockClustersSprawl One dense solid stack. Theme ClassicBoldSoftShadedNavyIndigoSkyTealEmeraldForestPlumBerryCrimsonEmberAmberCocoa **Customise colours** Figure Page background Style StandardClean Clean drops the title band and footer, leaving the figure. Generate puzzlePrint / save PDF 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. [Build the full book](https://app.oncebooks.com/publisher-studio/spatial/edit?from=spatial&v=2&s=eyJmYW1pbHkiOiJjb3VudC1jdWJlcyIsImRpZmZpY3VsdHkiOiJIQVJEIiwiY29sb3JUaGVtZSI6eyJ0aGVtZUlkIjoiY2xhc3NpYyIsIm92ZXJyaWRlcyI6e319fQ) Free to build · pay once to export Preview The puzzle and its answer, as they print. Hide the preview - Puzzle Hard How many cubes make up this figure — including the ones you cannot see? 1 Puzzle - Puzzle Hard · Answer 108 cubes 2 Answer Generate puzzlePrint / save PDF 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 1. Count 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. 2. Add 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. 3. Check 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 - [3D to flat Draw the views A solid drawn in 3D, with arrows marking the top (T), front (F) and side (S), and three empty grids beside it.](https://www.oncebooks.com/spatial-puzzles/draw-the-views) - [Flat to 3D Build the solid Three filled-in views, top, front and side, and a sheet of isometric paper below them to draw on.](https://www.oncebooks.com/spatial-puzzles/build-the-solid) ## Making a whole puzzle book? This page makes one puzzle. To publish a book on Amazon KDP, the [KDP spatial puzzle maker](https://www.oncebooks.com/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 - [Cube counting puzzles](https://www.oncebooks.com/spatial-puzzles/cube-counting) - [Draw the views puzzles](https://www.oncebooks.com/spatial-puzzles/draw-the-views) - [Build the solid puzzles](https://www.oncebooks.com/spatial-puzzles/build-the-solid) - [Easy cube counting puzzles](https://www.oncebooks.com/spatial-puzzles/easy) - [Expert cube counting puzzles](https://www.oncebooks.com/spatial-puzzles/expert) - [Spatial reasoning puzzles for kids](https://www.oncebooks.com/spatial-puzzles/for-kids) [See every printable spatial puzzle](https://www.oncebooks.com/spatial-puzzles) ## Questions **Are these hard cube counting puzzles 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 hard cube counting puzzles 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.