Block Counting Test

Counting the cubes on the screen one by one is slow and it is also wrong. The picture is missing some of them.

The way through is to stop counting cubes and start counting columns. Every square on the floor carries a column, and every column has a height you can read off its top face.

Add those heights and you have the pile. A four by four floor is sixteen numbers to add, and none of them is bigger than three.

That turns a picture problem into an adding problem, and adding is the part that goes wrong under pressure. You are holding a running total while working out the next number to add to it.

The amount of room that takes is the room a span test measures. The sizes are in a similar range: see how long a typical digit span is.

After every answer the height of each column is written on top of it. That is the method, printed on the pile you have just finished, rather than a mark out of ten.

Three faces of a cube point at you from this angle: the top, the face to the right and the face to the left.

A cube whose neighbours cover all three has nothing on the screen at all. It is not drawn faintly or drawn small. It is not drawn.

Every pile here is built so that at least one cube is in that position. The wide piles hide a good many more than one.

So a count of what you can see is always short. It is short by an amount you have to work out rather than look at. The result line after each pile says how many were buried.

This is the one rule the piles share with the stacks on the mixed spatial paper. Everything else about the two pages is different, starting with what you do about it.

Most cube counting items in a book of aptitude papers offer four numbers and ask you to pick one. That shape is convenient to mark and it carries a cost.

Four answers put a floor of about a quarter under everybody. A quarter of the marks on such a paper are inside reach of a coin, so a low score and a guessed score look alike.

There is nothing to pick between here. The box takes any number you type, so nothing arrives by luck and there is no floor to read the result against.

It also means a near miss is visible. Picking the wrong one of four is a zero whether you were one cube out or fifteen. Typing 23 when the pile holds 24 is plainly not the same event.

The cost of the open box is that you can type nonsense, and the score will believe you. A pile of twenty cubes answered 200 lands in the number as a miss of 180.

The headline is the size of your miss rather than a count of your misses. Every pile contributes the gap between what you typed and what was there.

Those gaps are added up over the run and divided by the piles in it, so the figure reads as cubes out per pile.

A middle value would be the usual choice on this site and it is the wrong one here. The per-pile gap is a small whole number with most of its weight on zero. A middle value reads 0 or 1 for nearly everybody, and hides the run that went badly.

The card also splits the misses by direction. Counting short means cubes you never accounted for, and counting over usually means a column double counted somewhere in the adding.

Time on a pile sits there too, as a middle value across the run. Nothing on this page is timed and nothing is scored on speed. Read it as a description of how you worked rather than as a result.

A run walks up a ladder. It opens on a two by two floor, moves to three by three, and finishes on four by four.

Cubes never go above three high at any point on that ladder, and holding the height fixed is deliberate.

A taller pile is more counting inside the same columns. A wider pile is more columns to hold, and the second of those is the thing this task is about.

The settings let you shorten the run to six piles or stop the floor at three squares across. Both make the same test easier rather than a different one.

The third setting is the one that changes the task. With empty squares allowed you can often see through a gap to the back of the pile. A solid floor closes that off and leaves nothing but the adding.

Most pages here put your result against a distribution. This one shows the number on its own, because there is no distribution to show it against.

Cube counting has been an item in aptitude batteries for the better part of a century. Nobody has published a distribution of the item itself.

What has been published belongs to whole papers, scored as a share of multiple-choice marks against a clock. None of that converts into cubes out per pile, and stretching it over this page would be an invented figure with a real citation attached.

Your own earlier runs are the fair comparison, and the page keeps them for you in this browser.

Practice moves this number quickly, and what improves is counting piles of cubes. How far anything like that travels beyond the task is argued over. The honest summary is in what brain training does and does not transfer to.

Our own norm is published when a thousand runs have been recorded here, and not one run before that.