Transitive Inference
Weigh the clues, deduce the answer
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What is the Transitive Inference?
Transitive inference is the ability to work out how two things compare when they have never been compared directly. If A is heavier than B, and B is heavier than C, you can conclude that A is heavier than C without weighing them together. Developmental psychologists have long studied when children can make this kind of deduction, and researchers also use transitive inference tasks to study relational reasoning in adults and in animals.
Transitive Inference on Neuroptimize turns this idea into a balance-scale puzzle. You see a few scales, each perfectly balanced with coloured shapes on both sides. No weights are given, so you must combine the clues to rank the shapes or to work out how many of one shape balance another. Every puzzle is checked to have exactly one correct answer.
How to play the Transitive Inference
- Each round shows a set of balanced scales. Every scale is level, so the shapes on the left weigh exactly the same as the shapes on the right.
- Below the scales is a question: which shape is the heaviest, which is the lightest, or how many of a given shape would balance a new scale. Tap your answer from the buttons at the bottom.
- A session has 8 rounds, and the dots at the bottom track your results. There is no countdown, but correct answers given quickly earn a small bonus, and your average answer time is shown at the end.
- At the start there are three shapes and only "heaviest" questions. "Lightest" questions arrive at level 5, and "how many balance this?" questions join from level 9.
- From level 11 a fourth shape is added, so you need an extra clue to pin down every weight. Higher levels also put more shapes in each pan, use a wider range of hidden weights, and sometimes add an extra clue scale to sort through.
Strategies and tips
Turn each scale into an equation
Read every scale as a simple sum, such as "one circle equals two squares". Writing the relationships in words, even silently, makes it much easier to combine them than trying to picture the scales.
Swap in the smallest unit
Pick the shape that looks lightest and express the others in terms of it. If a circle equals two squares and a square equals three triangles, then a circle equals six triangles, and the ranking falls out immediately.
Fewer shapes means heavier
When one shape balances several of another, the single shape is heavier. Use this quick check to narrow down "heaviest" and "lightest" questions before doing any arithmetic.
Cancel matching shapes
If you combine two scales and the same shape appears on both sides, it cancels out, just as it would on a real balance. This often turns a complicated pair of clues into a single clear comparison.
Solve the question scale last
For "how many balance this?" questions, first convert every shape on the question scale into the target unit, then add them up. The answer options sit close together, so a quick recount is worth it.
The science behind the Transitive Inference
Transitive inference is the ability to deduce the relationship between two items that have not been compared directly, for example concluding that A is heavier than C from knowing that A is heavier than B and B is heavier than C. It is studied as a form of deductive and relational reasoning.
Frequently asked questions
What is transitive inference?
It is the logical step of concluding that if A relates to B and B relates to C in the same way, then A relates to C. A classic example is working out that A is taller than C from knowing that A is taller than B and B is taller than C.
How do you solve balance scale puzzles?
Treat each balanced scale as an equation and substitute one shape for another until everything is expressed in the same unit. Then you can compare any two shapes or count how many of one balance a group of others.
Do I need to know the actual weights?
No. The game never shows weights, and you only need their relationships. Each puzzle is generated so that the clues lead to a single answer, whatever the exact weights are.
Is Transitive Inference a free game?
Yes, it is free to play. It unlocks once your Neuroptimize account reaches level 8.