Complete the Shape

You are shown the finished shape, and the same shape with a piece missing. You work out what the missing piece looks like, then pick it from the loose pieces.

A piece may be turned any way round, including tipped over onto another face. The big shape never moves at all. You slide your piece into it.

The whole question turns on one habit: build the hole first, before you look at a single piece.

The method

Five beats: find the bite, say the hole and count it, cross out on count, read the bend, try the tip.

1. Find the bite. Lay the two pictures side by side. Look for the step, notch or corner the finished shape has and the other has not. Nothing marks it for you — finding it is the first half of the question. Look before you subtract.
2. Say the hole and count it. Describe it out loud as a shape of its own. "An L: two along the bottom, one standing up at the left end." Now you are matching that object, not the two big piles. Then say how many cubes it holds: three, four or five. Count the hole, never the piles. A cube can sit hidden behind its neighbours, so a pile counted by eye comes out short. A hole you built in your head hides nothing.
3. Cross out on count. Every wrong piece but one is the wrong size. Of our 80, 55 are exactly one cube out and 9 are exactly double. That clears most of the board.
4. Read the bend. You will usually be left with two pieces the same size. Look along the hole's longest run and ask which way the short part goes. This beat has a name: the bend test. It is the check that decides 3D Rotation, on a smaller shape.
5. Try the tip. A piece often will not match until you lift it out of the flat and stand it on another face. Nine of our twenty answers need exactly that.

About 30 to 35 seconds each. An easy one takes 15.

Rules to watch

• Only the piece turns. Slide your piece in. Never turn the shape to help it fit.
• The hole is always three, four or five cubes. A count of one, of two, or of six or more means you have missed part of it. Go back and find the rest.
• A three-cube hole has no mirror. Any shape of three cubes or fewer is its own mirror image. So on those questions the bend test has nothing to catch. Four of our twenty are like that.
• Smallest is not a rule. On easier sets every wrong piece is bigger than the answer, so "pick the smallest" works and children learn it fast. Here the mirror is the same size as the answer.

Watch for these traps

We looked at all 80 wrong pieces in our twenty exam-level questions.

• One cube out. 55 of the 80, about three on every question. One cube added or one taken away, every time. Drawn solid, a five-cube piece and a four-cube piece look much alike. Counting the hole catches all 55.
• The mirror image. 16 of the 80, on 16 of the 20 questions. It is the only wrong piece that carries the hole's own cube count. So it is the piece left standing after you have counted, which makes it feel like the reward. Find the cube where the shape bends, and check which way the arm turns from there.
• The hole at double size. 9 of the 80, and every one is exactly twice the cubes. It is the right shape, and shape is what you have just described. It is never drawn smaller than the hole, so the count clears it too.

And one trap that is not there. The right piece at the wrong turn is never a wrong answer here. The question says a piece may be turned any way round. So a piece that matches once you have turned it is the answer. Other question types forbid turning, and children carry that rule across. Do not.

Stuck? Work down this list rather than guessing.

1. Count the hole and cross out. It works every time and removes most of the pieces.
2. Work one layer at a time. Compare the shapes bottom, middle, then top. The hole often falls out of a single level.
3. Compare heights. If the finished shape is one cube taller, the hole reaches the top layer.
4. Still nothing at 35 seconds? Choose on the bend even if you are unsure. The mirror is the piece that survives, so a half-sure bend call beats a guess.

Try these yourself

Now have a go yourself — tap the piece that completes the shape.

Related

• The complete 11+ question-type guide
• Building Blocks — which set of blocks builds the shape
• 3D Rotation — the same bend test, on the whole shape

All example questions come from the Brainblox question bank — practise this question type inside 15 arcade games, timed mock exams and focused practice. Brainblox is an independent app: not affiliated with, endorsed by or licensed by any exam board, school or assessment publisher, and it contains no past papers.