Simulations, puzzles &amp; tools

Coin pattern waiting times

Does heads–heads take longer than heads–tails?

Non-transitive dice

A beats B, B beats C… can D beat A?

Simpson’s paradox

Better in both groups. Worse overall?

Crowd wisdom and bias

Averaging removes noise. Does it remove bias?

Regression to the mean

Will the top performers stay on top?

Spot real randomness

Which dot pattern uses independent random points?

Wave interference

Two moving waves can add up to no wave.

Orbital period race

Double the orbital radius. How much longer is a year?

Rolling race

Race a solid sphere, solid cylinder and hoop.

Heavy and light drop

Does mass change the landing time?

Bounce speed vs height

80% rebound speed does not mean 80% rebound height.

Gear speed simulator

A larger driven gear turns more slowly—and backward.

Linear vs binary search

Watch a sorted list change the number of guesses.

More cores, limited speedup

Find the part of a job more cores cannot speed up.

Bandwidth vs latency

A faster connection still has to wait for the first byte.

Traffic shortcut paradox

Can adding a road make everyone slower?

Square–cube scaling

Double every dimension. How much bigger is the volume?

One extra metre of rope

Add a metre to a loop around a sphere. How high can it lift?

Meeting cost clock

Watch the time cost add up across a room.

Voting preference cycle

A beats B, B beats C, and C beats A?

The birthday paradox

How many people before a shared birthday becomes likely?

Does chance settle down?

Watch a coin’s running head rate wander towards its probability.

Why seven wins

Roll two dice and discover why their totals are uneven.

A walk without a plan

Follow one wandering path and see its displacement grow.

Order from falling beads

Drop beads through left-or-right decisions to build a bell-shaped pile.

Collect them all

Discover how the final missing collectible changes the wait.

The ruin experiment

Can a fair game still wipe out a small starting balance?

Streaks happen

Generate coin sequences and look for their longest runs.

Throw dots, find pi

Estimate π with random dots inside a square.

The average gets calmer

Compare individual random values with averages of larger samples.

The base-rate surprise

See how rare events change what a positive detector result means.

Why queues explode

Change arrival pressure and watch a single-server queue build up.

The compounding race

Watch deposits and growth separate over time.

The shrinking shopping basket

Watch a fixed cash amount lose purchasing power.

A little extra, paid sooner

Compare a fixed loan with and without monthly overpayments.

Aim, launch, explore

See how launch angle changes an ideal projectile’s path.

The pendulum’s secret

Compare swings as you change length and starting angle.

A spring in motion

Explore the rhythm of a mass on a spring.

Half, then half again

Watch a quantity shrink by repeated half-lives.

How a rumour spreads

Explore a simple growth curve as a story reaches a community.

Crack the sequence

Find the missing term in a generated arithmetic sequence.

Keep it balanced

Solve a generated linear equation and check both sides.

Make 24

Use all four cards once with arithmetic and brackets.

Call the percentage

Estimate a percentage before revealing the exact answer.

Which fraction wins?

Choose the larger fraction before the visual reveal.

Pick the better bag

Choose the bag with the better chance of drawing a gold counter.

The seating puzzle

Arrange four people using every clue.

The tower challenge

Move the tower one disc at a time without covering a smaller disc.

Across the river

Ferry a fox, goose and grain without leaving the wrong pair together.

Take the last counter

Take one, two or three counters; whoever takes the last wins.

Lights out

Turn every light off by toggling a cell and its neighbours.

Nine numbers, one sum

Place 1 through 9 so every row, column and diagonal has the same total.

Find the heavy coin

Find one heavier coin among nine using at most two balance weighings.

Crack the safe

Deduce a three-digit code from exact and misplaced matches.

The knight’s shortest route

Reach the marked square with a chess knight in as few moves as possible.

The number pad

Write an expression, keep a calculation history and reuse an answer.

Build a monthly budget

Change line items and see what is left to spend or save.

Compare two loans

See payments and lifetime interest side by side.

Plan a savings goal

Work out the monthly saving needed, then explore the balance over time.

Your data, made visible

Paste numbers to explore their spread, centre and distribution.

Fractions you can see

Add, subtract, multiply or divide two fractions, with a visual comparison.

The unit workbench

Compare one length across familiar units.

Mix to a ratio

Divide a total into any number of proportional parts.

Map out your time

Turn tasks into a sequential schedule with breaks.

Follow the percentages

Apply a chain of increases and cuts and see every step.

Compare your options

Score options against weighted criteria and inspect what drives the result.

Split the bill fairly

Assign individual spending, add a tip and see each person’s share.

Make balanced-size teams

Shuffle a list into teams and keep the result.

Find your break-even point

Move costs and prices to compare the route to break-even.

Sketch a function

Type a function of x and explore its sampled curve.