Canadian Innovation Math Contest · 2026

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Real CIMC contest problems, each paused for you to try, each ending with a named trick you can use again. Nineteen topics, 119 walkthroughs, sixteen foundation videos. The 2026 theme is Mathematics of Compassion.

121 videos

19 learning paths

0–7 levels

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The learning path

19 named tricks, sorted into 6 strands that climb from quick mental-math to deeper reasoning. New here? Start with Mental Math (Friendly Numbers), then climb each strand top to bottom — every strand opens with its easiest path.

Mental Math

Build fast, in-your-head number sense by reshaping numbers instead of computing the long way.

01 Mental Math · Friendly Numbers 7 videos ★ foundation
02 Mental Math · Multiplication Tricks 7 videos ★ foundation
03 Mental Math · Divisibility Rules 7 videos ★ foundation
04 Mental Math · Percent Sense 8 videos ★ foundation

Problem Solving

Turn a tricky story into an equation you can solve — by decoding, assuming, swapping, or undoing.

05 Substitution Arithmetic 6 videos
06 Chicken & Rabbit 7 videos ★ foundation
07 Excess & Shortage 7 videos ★ foundation
08 Working Backwards 8 videos ★ foundation

Patterns & Sums

Spot the rule inside a run of numbers, then sum or extend it without grinding through every term.

09 Gauss Technique 7 videos ★ foundation
10 Arithmetic Series 7 videos ★ foundation
11 Sequences & Series 7 videos ★ foundation

Counting Ways

Count gaps, arrangements, and shares systematically — without listing every case by hand.

12 Gaps & Intervals 6 videos ★ foundation
13 Permutations and Combinations 7 videos ★ foundation
14 Stars and Bars 7 videos ★ foundation

Shape & Space

Reason about length, angle, and area — then bridge from a picture to an algebraic identity.

15 Area Maze 6 videos
16 Geometry · Shape & Space 8 videos ★ foundation
17 Difference of Squares 7 videos ★ foundation

Reasoning & Data

Pull the decisive value off a chart, then find the best possible answer at a constraint’s edge.

18 Graphs & Data Interpretation 8 videos ★ foundation
19 Optimization · Greatest & Least 9 videos ★ foundation

01 · CIMC 2026 Mental Math

Mental Math · Friendly Numbers

Six lessons that all lean on the same habit — nudge an awkward number to a friendly base (ten, a hundred, a thousand), do the easy math, then settle up. Make Ten, Make Hundred, Round and Repay, Subtract Round Up, Make Thousand, Safe-Side Rounding.

★ Foundation 2:00 Like on YouTube

Bend and Repay — the One Habit Behind Fast Mental Addition

Sums like 9 + 6, 19 + 7, and 98 + 5 look awkward — but each hides a number that is one small step from a friendly base. 9 wants to be 10, 19 wants to be 20, 98 wants to be 100. The move: bend the number up to the base, do the easy math, then repay exactly what you nudged. Look for a number ending in 8, 9, 1, or 2 — that is the one begging for a base. This single habit powers every level of the Friendly Numbers series.

Peek the trick Hide the trick "Bend and Repay"

This idea grounds every problem in Mental Math · Friendly Numbers.

02 · CIMC 2026 Mental Math

Mental Math · Multiplication Tricks

Six lessons that all reshape one rectangle — bend a factor into a friendlier shape, do the easy multiply, then settle up. Double and Halve, Times-Five is Times-Ten Halved, Break Apart, Greatest Product Under a Cap, Times-Eleven, Squaring Near a Base.

★ Foundation 2:00 Like on YouTube

Factor Pairs — the One Habit Behind Fast Mental Multiplication

Products like 16 × 25 look heavy — until you notice the numbers are hiding friendlier factors. 25 is a quarter of 100, and 16 splits into 4 × 4. The move: break one factor into pieces, then regroup them with the other factor to land on a friendly number like 100. 16 × 25 becomes 4 × (4 × 25) = 4 × 100 = 400. Look for a factor that pairs with another to make ten, a hundred, or a thousand. This single habit powers every level of the Multiplication Tricks series.

Peek the trick Hide the trick "Factor Pairs"

This idea grounds every problem in Mental Math · Multiplication Tricks.

03 · CIMC 2026 Mental Math

Mental Math · Divisibility Rules

Six lessons that all read the answer straight out of the digits — no long division. Run the Rules, Find the Missing Digit, the Alternating-Sum test for 11, the 1001 = 7 · 11 · 13 block trick for 7 and 13, composite checks via coprime pieces, and a capstone that combines everything.

★ Foundation 2:00 Like on YouTube

Divisibility Rules — the Toolkit (and Why Each One Works)

Is 216 divisible by 6? Is 4095 divisible by 9? Most kids reach for long division — but every divisibility rule is a shortcut hiding in the digits. Powers of two and five only care about the END of a number: 2 looks at the last digit, 4 at the last two, 8 at the last three, 5 at the last digit. 3 and 9 care about the DIGIT SUM, because 10 leaves a remainder of 1. Knowing what each divisor actually "sees" powers every level of the Divisibility series.

Peek the trick Hide the trick "The Divisor Sees the Tail"

This idea grounds every problem in Mental Math · Divisibility Rules.

04 · CIMC 2026 Mental Math

Mental Math · Percent Sense

Seven lessons that take any percent of any number in your head — every percent built from a handful of friendly anchors carved straight off a bar. The seven anchors, scaling an anchor to any percent, stacking and unstacking, friendly-fraction percents, a percent of a percent, leaning on 100% for near-whole percents, and the swap that turns an ugly percent into an easy one.

★ Foundation 3:59 Like on YouTube

Percent Made Easy — Carve the Bar Into Anchor Slices

What is 25% of 240? What is 75% of 80? A percent is just a slice of a bar. Draw the whole as a bar and carve the slice you need: 50% is half, 25% is a quarter, 10% is a tenth. For 75%, quarter the bar and take THREE slices — never just divide by four. These anchor slices power every level of the Percent Sense series.

Peek the trick Hide the trick "Carve the Bar"

This idea grounds every problem in Mental Math · Percent Sense.

05 · CIMC 2026 Problem Solving

Substitution Arithmetic

Six problems where a custom symbol hides one operation. Decode the rule, substitute, compute.

Grade 2+ Level 0 2:11 Like on YouTube

The Star Button

A new button ✦ is defined by two examples. 2 ✦ 3 means 2 + 2 + 2 and 4 ✦ 2 means 4 + 4. What is 5 ✦ 4?

Peek the trick Hide the trick "Repeated Addition"

The symbol is multiplication in disguise. Decode that a ✦ b means a added to itself b times. Once you see the pattern, the answer is just a × b.

06 · CIMC 2026 Problem Solving

Chicken & Rabbit

One transferable technique — the Pretend Trick — wears new disguises across animals, vehicles, and shapes. Pretend everything is one kind, count what is missing, then swap to fix.

★ Foundation 1:55 Like on YouTube

The Pretend Method — When Two Kinds Mix

When a count mixes two kinds of things — chickens and rabbits, bikes and trikes, hexagons and triangles — and you know the total count plus the total "feet" (legs, wheels, sides), there is one trick that always works. Pretend everything is the cheaper kind. Count what is missing. Divide by the per-swap gap. That is how many to swap. The foundation for the entire Chicken & Rabbit series — every later level disguises the same single technique.

Peek the trick Hide the trick "The Pretend Method"

This idea grounds every problem in Chicken & Rabbit.

07 · CIMC 2026 Problem Solving

Excess & Shortage

Six disguises of one big idea — the bridge between two plans that share the same total. Leftover, shortage, swing, difference, adjustment, schedule.

★ Foundation 3:11 Like on YouTube

Excess and Shortage — The Two-Plan Bridge

When the same supply is distributed two different ways — and one plan leaves leftovers while the other runs short — the gap between the plans hides the number of recipients. Add the leftover and the shortage together, divide by the per-person difference, and the answer falls out. The foundation for the whole Excess & Shortage series.

Peek the trick Hide the trick "The Two-Plan Bridge"

This idea grounds every problem in Excess & Shortage.

08 · CIMC 2026 Problem Solving

Working Backwards

Seven problems that climb from a one-step undo (Level 0) to a capstone where three constraints filter down to one unique answer (Level 6).

★ Foundation 2:51 Like on YouTube

Working Backwards — Undo the Chain

When a story tells you what happened step by step and gives you the FINAL state, you do not have to guess what was at the start. Every forward operation has an inverse — plus becomes minus, multiply becomes divide. Walk the chain backward, applying each inverse in reverse order — last op first. The foundation for the whole Working Backwards series.

Peek the trick Hide the trick "Reverse the Operations"

This idea grounds every problem in Working Backwards.

09 · CIMC 2026 Patterns & Sums

Gauss Technique

Six contest problems built on the Gauss pairing trick. Pair first and last, count the equal pairs, multiply. From tiny direct pairing at L0 to a hidden repeating signed block at L5.

★ Foundation 2:45 Like on YouTube

Mental Math Challenge — How Carl Gauss Added 1 to 100

Add every whole number from 1 to 100. In 1786, nine-year-old Carl Friedrich Gauss solved this in under a minute. This is the trick that comes back in the Gauss-Technique series and again in Sequences & Series.

Peek the trick Hide the trick "Gauss pairing"

This idea grounds every problem in Gauss Technique.

10 · CIMC 2026 Patterns & Sums

Arithmetic Series

Six problems that hide an arithmetic sequence behind a story. Find the constant step, then formula or Gauss-pair your way to the answer.

★ Foundation 2:12 Like on YouTube

Gaps and Pairs — How Arithmetic Series Work

Two ideas, no formula required. Maya builds a 10-step block staircase. Find the GAP — every step grows by the same amount, so one number predicts any step. Then make a PAIR — copy the staircase, flip it upside down, slide it on top, and the two staircases form a perfect rectangle. Half of the rectangle is the answer. Grade-3 friendly visual proof that powers every level of the Arithmetic Series toolkit.

Peek the trick Hide the trick "Gaps + Gauss pairing"

This idea grounds every problem in Arithmetic Series.

11 · CIMC 2026 Patterns & Sums

Sequences & Series

Six problems that climb from spotting a pattern (Level 0) to combining two named techniques (Level 5).

★ Foundation 2:45 Like on YouTube

Mental Math Challenge — How Carl Gauss Added 1 to 100

Peek the trick Hide the trick "Gauss pairing"

This idea grounds every problem in Sequences & Series.

12 · CIMC 2026 Counting Ways

Gaps & Intervals

Five problems that all hide the same off-by-one move (N posts → N − 1 gaps). Each level disguises it a different way — counting tiles, measuring distance between numbered points, dividing time, subtracting forbidden positions, and equating two plans on one corridor.

★ Foundation 1:53 Like on YouTube

Posts and Spaces — Foundation of the Gaps & Intervals Toolkit

Hold up your hand. Five fingers — but only FOUR gaps between them. Posts and spaces are different. N items in a line with one at each end give N − 1 spaces between them. Always. Maya wants to plant 4 trees evenly along a 12-meter path, one at each end. It is NOT 12 ÷ 4 — count the GAPS (3), not the trees. 12 ÷ 3 = 4 m. Once you see it on your hand, the same trick unlocks every level of the Gaps & Intervals series — fence posts, water stations, shuttle times, lantern routes, two-plan corridors.

Peek the trick Hide the trick "Posts and Spaces"

This idea grounds every problem in Gaps & Intervals.

13 · CIMC 2026 Counting Ways

Permutations and Combinations

Six counting problems themed around a school welcome day — lining up students, pairing buddies, choosing committees, building an outreach team. Each level adds one named tool to the toolkit; L5 chains them all in a single problem.

★ Foundation 4:52 Like on YouTube

What are Permutations and Combinations? — When Order Matters and When It Doesn't

Three counting tools cover almost every kid-friendly counting problem: FACTORIAL for lining things up, PERMUTATION for picking in order, COMBINATION for picking without order. We derive each one from a small concrete example — 3 friends in a photo line gives 3! = 6, picking 3 captains from 5 players in order gives P(5,3) = 60, picking a team of 3 from 5 with no order gives C(5,3) = 10. End with a one-question decision tree: "if I swap two of the picks, is it the same answer?" YES → combination, NO → permutation. Prerequisite for the Welcome Day series.

Peek the trick Hide the trick "Factorial · Permutation · Combination"

This idea grounds every problem in Permutations and Combinations.

14 · CIMC 2026 Counting Ways

Stars and Bars

Six distribution problems that ask how many ways identical items can be shared across distinct rooms under varying constraints. Each level adds one named tool to the toolkit; L5 chains them all in a single problem.

★ Foundation 2:57 Like on YouTube

What is Choose? — Compute n choose k With a Simple Shortcut

Where does CHOOSE show up — teams, pizza toppings, lottery tickets? And how do you compute 6 choose 2 or 5 choose 3 without a calculator? Start by listing pairs of 4 friends, then derive the shortcut formula: top k of n, divided by k down to 1. The prerequisite for the Stars and Bars series.

Peek the trick Hide the trick "top k of n, divided by k!"

This idea grounds every problem in Stars and Bars.

15 · CIMC 2026 Shape & Space

Area Maze

Six composite-rectangle puzzles with most side-lengths hidden. Each level adds one named tool to the toolkit; L5 chains them all in a single figure.

Grade 2+ Level 0 2:01 Like on YouTube

Two Rectangles, One Wall

A reading-corner mat is made from two rectangles in a row. The left has area 12 cm² and is 3 cm wide. The whole row is 8 cm wide. Find the area of the shaded rectangle on the right.

Peek the trick Hide the trick "Shared Side"

Two rectangles glued along the same wall must share that wall’s length. Use area ÷ known side on one rectangle; the other rectangle inherits the side for free.

16 · CIMC 2026 Shape & Space

Geometry · Shape & Space

Geometry shows up everywhere — but the same handful of habits unlock most problems: name the measure, read the words and draw what they say, chain angle facts, and let equal sides do their work. Seven lessons build one practical toolkit: count the outside edges, cut perimeter in half, lay base × height for rectangles and right triangles, turn words into a figure and chain angle facts, use the polygon angle rule, unlock parallel proportional sides, then finish as the Angle Detective inside a circle.

★ Foundation 2:07 Like on YouTube

Name the Measure — Length, Angle, or Area? (Geometry Foundation)

Every geometry question first asks: WHICH measurement does the answer want? Length, angle, or area? Mixing them up is the most common mistake. The same rectangle can answer all three — but with totally different numbers and units. Length lives on the edge, angle lives at the corner, area lives inside. Name the right one and the whole solution gets simpler.

Peek the trick Hide the trick "Name the Measure"

This idea grounds every problem in Geometry · Shape & Space.

17 · CIMC 2026 Shape & Space

Difference of Squares

One algebraic identity, seven videos. a² − b² = (a+b)(a−b) — taught visually with quilt patches, then applied under progressively-disguised setups from "count the new border" at L0 to "factor + double-filter" at L5.

★ Foundation 2:48 Like on YouTube

The Two-Squares Trick — Why a² − b² = (a + b)(a − b)

A visual proof that the difference of two squares always factors. Cut the corner off an a×a square and rearrange — the L-shape becomes an (a+b)×(a−b) rectangle. This single identity drives every level of the Difference-of-Squares series.

Peek the trick Hide the trick "a² − b² = (a + b)(a − b)"

This idea grounds every problem in Difference of Squares.

18 · CIMC 2026 Reasoning & Data

Graphs & Data Interpretation

A graph is data in disguise. Seven lessons teach the one habit every graph question needs: read the axes and the scale first, pull the exact values you need, then do the math. Combine a chart with a sentence-clue, decode a tricky scale, compare a double bar, read the jump on a line, subtract on a running total, link two graphs for a rate, and chain the reads like a data detective.

★ Foundation 1:59 Like on YouTube

How to Read a Graph: Find the Scale First

A graph is data in disguise. Before you read a single bar, you have to know what one square is worth — on a chart where one square stands for 5 bottles, a bar four squares tall is 20, not 4. A bar is worth its height in squares times the scale: the graph stores the data, you do the math. The reading skill the whole Graphs path is built on.

Peek the trick Hide the trick "Read the Scale"

This idea grounds every problem in Graphs & Data Interpretation.

19 · CIMC 2026 Reasoning & Data

Optimization · Greatest & Least

Nine lessons that turn "greatest" and "least" problems into a toolkit. Name the objective you push and the constraint that stops it, then find the answer right at the edge: the bottleneck rule, greedy biggest-first, squeezing the rest, rounding up to guarantee, shaping the extreme, testing the boundary, pushing the right corner, and the detective habit that picks the right tool.

★ Foundation 2:52 Like on YouTube

Greatest or Least? How to Spot an Optimization Problem

What makes a problem an optimization? When you see "the greatest number of kits" or "the smallest budget," you are not just calculating — you are pushing one quantity as far as a limit allows. Every such problem has an OBJECTIVE you push and a CONSTRAINT that stops it, and the best answer sits right at the edge where they meet.

Peek the trick Hide the trick "Objective vs Constraint"

This idea grounds every problem in Optimization · Greatest & Least.