Connecting Shapes

Three or four grey pieces are shown, and some of their edges carry letters. You pick the picture of the shape the pieces make.

The letters mark joins, not pieces. Each letter sits on two edges, on two different pieces, and those are the edges that meet.

So the pieces make a chain. Only a piece in the middle of the chain carries two different letters.

The method

Five beats: count the letters and name the middle, find each twin, turn the others to meet it, say the shape, check the pieces are yours.

1. Count the letters and name the middle. Three pieces, two letters. Four pieces, three letters. If you cannot find a letter's twin, you have missed a piece. Then name the middle: it is the piece carrying two different letters. With four pieces there are two middles. Everything is built round them.
2. Find each twin. Point at a letter, then at the edge sharing it. This beat has a name: the twin edge. Those two edges become one, and it vanishes inside the finished shape.
3. Turn the others to meet it. Hold the middle piece exactly as it is drawn and bring the outside pieces to it. Say each turn out loud: "a quarter turn clockwise", "upside down". A piece may turn on the spot. It may never be turned over.
4. Say the shape. One sentence, before you look at a single picture: "a bracket opening to the left, with a step on top". Deciding first stops a near miss talking you round.
5. Check the pieces are yours. Last look before you answer. Are all the pieces you were given really in there?

About 25 to 35 seconds each. These are among the slowest on the paper.

Rules to watch

• Every join edge is straight and one square long. What varies is which way a piece must turn to bring that edge round.
• Turning is allowed. Turning over is not. A piece keeps the same shape when it turns. Turned over, it becomes a different piece.
• Nothing overlaps and nothing is lost. The finished shape holds exactly as many squares as the pieces do together, in all twenty of our exam-level questions.
• But counting squares decides almost nothing. 64 of our 80 wrong pictures hold the right square count. Counting catches one family only.
• Hold the middle piece still. You may keep any one piece where it is, so keep the one with two letters. Turning that one means turning everything else to match.
• Expect three or four pieces. Easier practice sets use two, which needs no chain. Every exam-level question here uses three or four.

Watch for these traps

We looked at all 80 wrong pictures in our twenty exam-level questions. They share out evenly: five families, each used exactly 16 times. None is rarer than another, so all five are worth knowing.

• Joined on the wrong edges. The right pieces, in a sensible arrangement, meeting where no letter said. It usually looks tidier than the real answer. Beat 2 is the guard: point at the letter, then at its twin, then at the picture.
• A piece turned to the wrong angle. The right edges really do meet, but one piece sits a quarter turn out, so the rest of it points the wrong way. Look at the far end of that piece: the joined end is right in every picture, so it can never tell them apart.
• Turned over instead of turned round. One piece flipped, or the whole shape drawn as a mirror. On a table, flipping a piece feels like the same sort of move as turning it. Pick one piece that has a left and a right, and check it is still the same way round.
• A piece you were never given. One piece swapped for a near twin — a straight bar in place of a corner. It holds the right number of squares, so counting is no help, and nobody re-checks the pieces once the layout looks right. That is beat 5.
• Squashed together. One piece pushed a square into its neighbour instead of meeting it edge to edge. This is the only family counting catches, and it is easy: every one of the 16 comes out exactly one square short.

Stuck? Work down this list rather than guessing.

1. Count the squares once. Cross out the picture that is one short. Then stop counting.
2. Join just two pieces. Do the first letter only, and see which pictures contain that pair.
3. Hold each picture against the pieces on the left and hunt the one you were never given.
4. Still nothing at 25 seconds? Pick from what is left and move on. Do not start again — a second go almost always repeats the first.

Try these yourself

Now have a go yourself — tap the shape that the pieces make.

Related

• The complete 11+ question-type guide
• Hidden Shapes — the same ordered tracing, on a busy figure
• Complete the Shape — find the piece that fills the gap

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.