Practice

Mental math practice

Calculations, missing numbers, estimation and everyday problems, with worked methods and an optional timer.

10 untimed questions · 2- or 8-minute sprint

Skills: Arithmetic

Switch or stay

Open the doors, inspect the host’s rule and test when switching really helps.

3 steps · 3 levels · Untimed

Skills: Probability and counting

When averages mislead

Change the group sizes and watch the overall winner change.

3 steps · 3 levels · Untimed

Skills: Tables and charts · Numerical reasoning

Reading comprehension

Read a passage against a clock, then answer four questions about it.

1 passage · 4 questions · 5 levels

Percentages

Calculate percentages, changes and original values.

10 questions · 3 levels · Untimed

Skills: Fractions and percentages · Arithmetic

Risk and reward

Try point games and discover when a big prize, a better average and a better chance mean different things.

3 steps · 3 levels · Untimed

Skills: Probability and counting · Numerical reasoning

Correlation detective

Uncover a hidden line by removing planted anomalies from a scatterplot.

3 steps · 3 levels · Untimed

Skills: Tables and charts

Word search

Find hidden words. Start with a word list, or solve their clues.

6–10 words · Word list or clues · No time limit

Times tables

Answer twenty multiplication facts, then see which ones are still slow.

20 facts · 15 sets · Optional 5 second clock

Reason with probability

Compare outcomes, follow dependent draws and find expected point values.

8 questions · 3 levels · Untimed

Skills: Probability and counting

Data interpretation

Read tables and charts, then compare values, find means or calculate percentages.

6 questions · 3 levels · No time limit

Skills: Tables and charts · Numerical reasoning

Reading skills

Eight short passages with one question each: main idea, inference, detail or word meaning.

8 passages · 1 question each · English

Note reading

Name the note written on the staff. Treble clef, bass clef and ledger lines.

6 questions · 3 levels · No time limit

Fractions and decimals

Calculate with fractions and decimals, or build targets with fraction pieces.

10 questions or a workshop · 3 levels

Skills: Fractions and percentages · Arithmetic

Counting combinations

Count choices, codes, groups and routes by checking order and repeats.

6 questions · 3 levels · No time limit

Skills: Probability and counting · Numerical reasoning

Distributions

Reason about averages, medians, spread and outliers. Change a data value to see which conclusions still hold.

1 question · 3 levels · Untimed

Skills: Tables and charts · Numerical reasoning

Deep reading

Read a longer passage, connect ideas, and test your interpretation against the evidence.

Self-paced · Evidence review

Compare quantities

Compare number quantities using arithmetic, fractions, percentages and powers.

9 questions · 3 levels · Untimed

Skills: Comparing quantities · Fractions and percentages

Conditional probability

Work through restricted sample spaces, linked selections and conditional events. Explore the counts behind each answer.

1 question · 3 levels · Untimed

Skills: Probability and counting · Numerical reasoning

Sampling

Compare weighted populations and sampling methods. Separate a method’s bias from variation in individual samples.

1 question · 3 levels · Untimed

Skills: Tables and charts · Numerical reasoning

Verbal reasoning

Judge statements as true, false or cannot say using only a short passage.

6 questions · 3 levels

Mirror images

Find the reflected shape among rotations and close copies.

6–9 squares · 8 levels · No time limit

Skills: Reflection

Number sequence puzzles

Find the next number, fill a grid, or untangle two sequences.

6 questions · Explanations · Optional 2-minute challenge

Skills: Numerical reasoning

Birthday collisions

How small can a group be before matching birthdays become likely? Predict, generate groups and inspect the matches.

3 steps · 3 levels · Untimed

Skills: Probability and counting · Numerical reasoning

Signal or chance?

Shuffle group labels to discover how surprising a difference really is.

3 steps · 3 levels · Untimed

Skills: Tables and charts · Numerical reasoning

Text completion

Use the meaning of a short English passage to choose the words that complete it.

3 questions · 3 levels · English

Hidden figures

Find a small figure hidden among extra lines.

5 choices · 8 levels · Untimed

Skills: Shape comparison

Make 24

Merge four cards two at a time and make the last one 24. Fractions are allowed.

6 deals · 3 levels · Undo · Hint

Skills: Arithmetic · Numerical reasoning

Pattern races

Race coin patterns and discover why equally likely sequences can have different waiting times.

3 steps · 3 levels · Untimed

Skills: Probability and counting · Numerical reasoning

Confidence intervals

Draw repeated samples and discover which intervals capture the true mean.

3 steps · 3 levels · Untimed

Skills: Tables and charts · Numerical reasoning

Sentence equivalence

Choose two words that fit an English sentence and give it the same meaning.

3 questions · 3 levels · English

Kakuro

Fill each run with different digits from 1 to 9 to make its clue total. Crossing runs share a digit.

1 puzzle · No time limit

Nontransitive dice

Find dice that beat one another in a cycle, then test how rolling twice changes the best response.

3 steps · 3 levels · Untimed

Skills: Probability and counting · Numerical reasoning

The comeback illusion

Retest unusually high or low scores and separate real change from chance.

3 steps · 3 levels · Untimed

Skills: Tables and charts · Numerical reasoning

Synonyms in context

Read a sentence and choose what the marked word means there.

6 questions · Untimed · English

Memory Palace

Connect five objects to familiar places, then return to recall the same set.

5 objects · Untimed · Saved reviews

Angle ranking

Put four angles in order from smallest to largest, then align them to compare.

5 questions · 3 levels · Untimed

Skills: Shape comparison

Estimate and compare

Round to useful benchmarks and choose the closest of five answers.

8 questions · 3 levels · Untimed

Skills: Arithmetic · Numerical reasoning

Chance bounds

Use incomplete counts to decide what must, might or cannot be true about chance.

6 questions · 3 levels · Untimed

Data conclusions

Decide whether a claim follows from incomplete records, conflicts with them, or needs more information.

6 questions · 3 levels · Untimed

Word ladder

Turn one word into another by changing one letter at a time. Every step has to be a real word.

5 ladders · 3 lengths · Shortest ladder counted · Hint

Find the missing number

Type the number that fills the blank in each equation.

10 items · 4 levels · A clock on each item

Probability paths

Compare routes that can fail, notice shared bottlenecks and choose useful upgrades.

6 questions · 3 levels · Untimed

Match the chart

Find the chart that preserves a table's category labels, values, units and series.

6 questions · 3 levels · Untimed

Fast multiplication

Multiply two digit numbers by a method instead of long multiplication.

10 questions or a 3 minute sprint · 4 levels

Area builder

Build connected shapes with a fixed area. Match a target perimeter, or find the smallest or largest possible perimeter.

1 puzzle · 3 levels · Untimed

Stop or continue

Use a changing deck to decide whether another draw is worth taking.

6 questions · 3 levels · Untimed

Choose the comparison

Choose a study plan that separates the target effect from other differences.

6 questions · 3 levels · Untimed

Squares and roots

Type the square, the cube or the root from memory.

12 items · 4 levels · Untimed or a 2-minute sprint

Make chance fair

Build equal chances from independent flips with an unknown bias.

6 questions · 3 levels · Untimed

Check the forecast

Compare how probability forecasts match observed frequencies, separate groups, and score their errors.

6 questions · 3 levels · Untimed

Unit conversion

Convert between metric and imperial units, then check the result against an anchor.

6 questions · 3 levels · Untimed

Shape classification

Infer a shared geometric relationship from three examples, then choose the new figure that belongs.

6 questions · 3 levels · Untimed

Chance over steps

Follow one token through rooms and combine the probabilities of different routes.

3 levels · Guided practice

Fit the line

Fit observations, predict from the line and interpret the limits of the prediction.

3 levels · Guided practice

Letter path

Find the long word that runs through every square of a letter grid, with some letters missing.

5 words · 4 levels · Hint

Ratios & averages

Divide amounts in a ratio and find averages across unequal groups.

8 questions · 3 modes · Untimed

Skills: Ratios and rates · Numerical reasoning

Figure counting

Count every triangle or rectangle in a line diagram, including larger figures made from smaller regions.

6 questions · 3 levels · Untimed

Word parts

Prefixes, suffixes and roots. Say what a part means, find the word that has it, or work out a whole word from its parts.

8 questions · 3 levels · English

Recall Map

Read a short passage, recall its connected ideas, and check what you remember later.

5 ideas · Untimed · Saved reviews

Region queens

Place one queen in each row, column and region. Queens must not touch, even at a corner.

1 puzzle · No time limit

Speed & work rates

Convert time units, compare speeds and combine work rates.

8 questions · 3 modes · Untimed

Skills: Ratios and rates · Arithmetic

One-stroke figures

Use every line once. Reason about connections, endpoints and the effect of adding one line.

6 questions · 3 levels · Untimed

Exam word problems

Salt water, speed, work rate and counting cases, in the shape aptitude tests ask them.

6 questions · 3 levels · Untimed

Skills: Ratios and rates · Fractions and percentages · Numerical reasoning

Shortest surface routes

Unfold a box to compare exact distances across its faces, then fold each route back onto the solid.

6 questions · 3 levels · Untimed

Algebra: Equations & inequalities

Solve equations and describe full solution sets, from linear steps to systems, quadratics and rational inequalities.

6 questions · 3 levels

Two running counts

Keep separate totals as shapes appear one at a time.

2–3 min

Skyscrapers

Place towers so each clue counts the towers seen from its side. Taller towers hide shorter ones.

1 board · No time limit

Algebraic expressions

Recognize equivalent expressions by collecting terms, factoring, using exponent rules and preserving domain restrictions.

6 questions · 3 levels

What changed?

Look at a few everyday things, then pick the one that is gone, moved or swapped.

6 questions · 4 levels · No time limit

Numbers around the center

Identify a briefly shown number while looking toward a central marker.

2 min

Functions & graphs

Read graphs and reason through function composition, transformations, inverses and domains.

6 questions · 3 levels · Untimed

Mini crossword

Solve a small crossword on one everyday theme. Type each answer to fill the grid.

6–10 words · 12 themes · Hints · Print

Picture details

Study a picture of everyday things, then answer questions about it: what was there, how many, what color and where.

2 pictures · 4 levels · No time limit

Quick look

Take in more at a glance: a shape in the middle and a star around it.

24 looks · 5 levels · Answers untimed

Tile pairs

Match identical free tiles and clear the tray. Every symbol stays visible.

1 puzzle · No time limit

Compare quantities: Variables

Prove an algebraic comparison or find allowed values that change the answer.

6 questions · 3 levels · Untimed

Category list

Pick an everyday theme and name as many things in it as you comfortably can.

13 themes · Untimed · 60 seconds if you like

Find the pairs

Turn over two cards at a time to find the matching pairs of everyday pictures.

6, 8 or 12 pairs · 3 levels · No time limit

Spot the differences

Two versions of one picture of everyday things, side by side. Tap each place where they differ.

3 pictures · 4 levels · No time limit

Nonograms

Use the numbered runs to find the filled squares. Mark the empty squares and reveal a picture.

1 puzzle · No time limit

Number properties

Explore factors, multiples and remainders with short whole-number questions.

6 questions · 3 levels · No time limit

Skills: Arithmetic · Numerical reasoning

Story order

Read a short story, then put its events in the order they happened.

3 stories · 3 levels · Untimed

List recall

Study a short shopping list, then pick its items from a larger set of pictures.

5, 7 or 10 items · 3 levels · No time limit

Two-hand tracing

Trace two shapes at once with a finger of each hand, or one at a time with a mouse.

4 pairs · 3 levels · No time limit

Futoshiki

Use each number once in every row and column. The inequality signs tell you which neighboring number is larger.

1 puzzle · No time limit

Number bases

Read a number in one base and write it in another.

12 questions · 4 levels · Untimed or a 2-minute sprint

One moment, one story

Remember or imagine a small moment. Tell it in your own words, alone or with someone.

3 or 5 optional prompts · No time limit

Everyday cue cards

Make a useful reminder, then use it to finish a small task.

3 or 6 everyday tasks · At your pace

Find it in the painting

Look at one large painting from The Met and find the details on a list, such as a dog, a red jug or a boat.

5–8 details · 12 paintings · Hints · Magnifier · Print

Binary logic grids

Balance zeros and ones in each row and column. Avoid three matching symbols consecutively, and do not duplicate a row or a column.

1 puzzle · No time limit

Quant interview arithmetic

Answer as many short questions as you can before the clock runs out.

10 kinds of question · Typed answers · Wrong answers cost a point

Find a word with clues

Explore an everyday word through its use, details and beginning.

No timer. Open any clue you need.

Pick up where you left off

Leave a clear checkpoint, take a short pause, and return to the next unfinished step.

3 tasks · No timer · Keep your checkpoint

Notice around you

Pause to notice a few ordinary details in your surroundings.

At your pace · No score

Connect the pairs

Give every pair a path. Plan the turns, protect the narrow gaps, and leave room for the other letters.

One puzzle · Untimed · Hints available

Number challenges

Solve number problems with hints and worked solutions. Extended rounds add digit constraints and missing digits in squares and cubes.

4 challenges · 3 levels · Worked solutions

Skills: Arithmetic · Numerical reasoning

Give clear directions

Describe an arrangement, then follow the message to rebuild it. Try it alone or take turns with someone.

3 arrangements · No time limit

Where did that come from?

Remember a detail and the message or notice where you read it.

3 situations · Self-paced study · Answers explained

Mirror paths

Turn mirrors to guide a beam through its checkpoints and into the target.

1 puzzle · 3 levels · Untimed

Cover the grid

Draw one route through every open cell. Keep a way into unfinished areas and plan where the route will end.

One puzzle · Untimed · Hints available

Clock and calendar

Read clock faces, work out how long things take, and find days and dates on a calendar.

6 questions · 3 levels · Untimed

Ask the missing question

Clarify an everyday plan, then check that you understood.

Untimed. Ask, listen to the reply, then confirm the plan.

Keep track of changes

Remember the latest assignment as a few details change.

3 situations · No timer

Plan the errands route

Visit the right places in a useful order. Adapt to closures and opening times.

3 levels · Guided practice

Rectangle regions

Divide the grid into rectangles. Each number tells you how many cells its rectangle must contain.

One puzzle · Untimed · Hints available

Large-number arithmetic

Work through bigger calculations, one useful step at a time.

At your pace · Exact whole-number answers

Listen and act

Listen for the request, notice a correction, and choose the next action.

3 levels · Guided practice

Light up

Place bulbs to light every white cell. Use wall numbers and light paths to decide where each bulb belongs.

One puzzle · Untimed · Hints available

Prime or not?

Make a quick decision, then discover the factors behind each answer.

Yes or no · Every answer explained

Remember to do it later

Form a plan, switch to another task, and remember to act when the right moment arrives.

3 levels · Guided practice

Islands and sea

Each number is the size of its island. Mark the sea around them, all in one piece.

1 board · No time limit

Reshape a calculation

Make the numbers easier while keeping the answer the same.

At your pace · Integer arithmetic

Sentence span

Judge sentences while remembering their final words in order.

3 levels · Guided practice

Bridge the islands

Connect numbered islands with straight bridges. Match each number and keep every island connected.

One puzzle · Untimed · Hints available

Rebuild the story

Reconstruct the order of everyday events and check what the story actually establishes.

3 levels · Guided practice

Make one loop

Draw lines between dots to make one closed loop. Each number tells you how many sides of its square need a line.

One puzzle · Untimed · Hints available

Shop within a budget

Compare pack sizes, quantities, and offers to build a basket that meets the brief.

3 levels · Guided practice

Build a vector

Combine two arrows using positive, negative and fractional multipliers. Explore which targets are reachable.

3 levels · Guided practice

Card patience

Build each suit from ace to king. Every card is face up, so planning decides, not luck.

26 or 52 cards · Every deal checked · Hints

Push the boxes

Push each box onto a target. You can push but never pull, so plan before you move.

1 board · No time limit

Compass relations

Follow a chain of clues and place one location relative to another.

3–5 min

Scheduling & resource allocation

Fit tasks into a timetable. Work around room availability, task lengths and dependencies.

3 plans · 3 levels · No time limit

Sort into groups

Put everyday things into two or three groups: by kind, fruit or vegetable, how they move, or color.

3 sets · 4 levels · No time limit

Move into place

Move, match and sort everyday things.

Drag or tap

Color mixing

Predict a mixture, find a missing color, and follow the light through filters.

6 questions · At your pace

Check before you act

Look for a useful clue in a message, then choose how to check it.

Untimed · Clues, choices and explanations

Many uses for one object

Find a use for something familiar. Change its purpose, then reshape an idea to fit a limit.

One object · Two ideas · No time limit

Find it in fewer checks

Open an ordered drawer, compare its number, and narrow down where your target can be.

3 levels · Guided practice

Sort with a strategy

Order a row of cards by making one clear comparison at a time.

3 levels · Guided practice

Follow the rule

Check each condition, then choose the branch it leads to.

3 levels · Guided practice

Manage the waiting line

Follow each arrival and removal. The rule decides who leaves next.

3 levels · Guided practice

Repair a worked solution

Find the first step that goes wrong, repair it, and use the method on a new problem.

3 levels · Guided practice

Scene repair

Locate a broken connection or sequence and choose the smallest repair that works.

3 levels · Guided practice