Square numbers 1-20 bingo
Square numbers 1-20 bingo uses 20 problems (x² for every x from 1 to 20), whose 20 different answers fill 4x4 cards. The caller reads "11²", players mark 121. With 30 cards the first bingo comes after about 6 calls.
196 | 100 | 256 | 4 |
169 | 49 | 400 | 25 |
121 | 16 | 289 | 1 |
144 | 81 | 9 | 36 |
The caller reads a problem; players mark its answer. 20 problems, 20 answers.
Free: up to 30 different cards per set. Pro: up to 1,000.
Free sets stop at 30 different cards. Your 30 cards are ready to print or download now.
Pro ($19 one-time) opens soon: up to 1,000 different cards per set and 2 or 4 cards on a PDF page. No payment is taken now.
Caller sheet
Every call in a shuffled order. Tick each one as you read it out; the same share link always gives the same order.
Updated
Square numbers 1-20 at a glance
| What is called | 20 problems: x² for every x from 1 to 20 |
|---|---|
| What is on the cards | 20 answers, from 1 to 400 |
| Recommended card | 4x4: 16 answers per card |
| Different cards possible | about 101 quadrillion (20 answers placed in 16 squares) |
| Typical level | Grade 5-6 |
| Problems per answer | one each |
Answer key: every square numbers 1-20 problem by answer
20 calls, 20 squares. First marked = (20 + 1) ÷ (problems + 1), the average call at which the answer is reached in a shuffled game.
| Answer | Problems the caller reads | Problems | First marked (avg. call) |
|---|---|---|---|
| 1 | 1² | 1 | 10.5 |
| 4 | 2² | 1 | 10.5 |
| 9 | 3² | 1 | 10.5 |
| 16 | 4² | 1 | 10.5 |
| 25 | 5² | 1 | 10.5 |
| 36 | 6² | 1 | 10.5 |
| 49 | 7² | 1 | 10.5 |
| 64 | 8² | 1 | 10.5 |
| 81 | 9² | 1 | 10.5 |
| 100 | 10² | 1 | 10.5 |
| 121 | 11² | 1 | 10.5 |
| 144 | 12² | 1 | 10.5 |
| 169 | 13² | 1 | 10.5 |
| 196 | 14² | 1 | 10.5 |
| 225 | 15² | 1 | 10.5 |
| 256 | 16² | 1 | 10.5 |
| 289 | 17² | 1 | 10.5 |
| 324 | 18² | 1 | 10.5 |
| 361 | 19² | 1 | 10.5 |
| 400 | 20² | 1 | 10.5 |
Self-check: square numbers 1-20 answers
- 1² = 1 × 1 = 1
- 3² = 3 × 3 = 9
- 5² = 5 × 5 = 25
- 6² = 6 × 6 = 36
- 7² = 7 × 7 = 49
- 8² = 8 × 8 = 64
- 11² = 11 × 11 = 121
- 13² = 13 × 13 = 169
- 14² = 14 × 14 = 196
- 15² = 15 × 15 = 225
- 16² = 16 × 16 = 256
- 17² = 17 × 17 = 289
- 19² = 19 × 19 = 361
Is square numbers 1-20 bingo fair?
In square numbers 1-20 bingo each of the 20 answers comes from exactly 1 problem, from "1²" (1) to "20²" (400), so every square on the card has the same chance: an answer is first marked at call 10.5 of 20 on average, and after 5 calls each one has a 25% chance of being marked.
With 20 calls in square numbers 1-20 bingo and 16 squares per card, every 4x4 card is full by call 20 at the latest, so the shuffle alone decides who shouts first.
How long a square numbers 1-20 game lasts
300 simulated square numbers 1-20 games (4x4, any line wins): 1 card needed 11 calls (median), 10 cards 8, 30 cards 6, with 8 in 10 games between call 5 and 8.
A class of 30 playing square numbers 1-20 bingo uses 30% of the 20 calls per game, so one caller sheet covers about 3 games; a full-card game with 30 cards took 18 calls.
How to play square numbers 1-20 bingo in class
-
Draw the squares
Sketch a square with side 14 on grid paper: the answer, 196, is what you count. The cards hold 20 answers from 1 to 400.
-
Hand out the cards
Print 4x4 square numbers 1-20 cards: 16 of the 20 answers (1 to 400) each, 80% coverage.
-
Read the problem, not the answer
Call "20²", pause, then the next. 20 calls, one per answer, so no square has a head start.
-
Check every bingo
Read back the called problems; the winner names each answer (14² → 196). 30 cards: first bingo near call 6.
Example calls from this set
Four problems drawn from the square numbers 1-20 caller sheet and the square each one marks.
-
The caller reads 1²
Mark 1 (the only problem with this answer)
-
The caller reads 14²
Mark 196 (the only problem with this answer)
-
The caller reads 6²
Mark 36 (the only problem with this answer)
-
The caller reads 7²
Mark 49 (the only problem with this answer)
Frequently asked questions
How many problems are in square numbers 1-20 bingo?
20 problems (x² for every x from 1 to 20), with 20 different answers. The caller sheet lists all 20; the cards show only the answers.
What size card works best for square numbers 1-20?
4x4. A card needs 16 different answers and the square numbers 1-20 set has 20 (1 to 400), so a 4x4 card is the largest that fits. That still allows about 101 quadrillion different cards.
Does any answer come up more often than others?
No. Each of the 20 answers is reached by exactly 1 problem of the 20 (1² gives 1, 20² gives 400), so every square has the same chance and is first marked around call 10.5 on average.
How many calls until someone wins?
In 300 simulated square numbers 1-20 games with 30 4x4 cards, the first line was completed after a median of 6 calls; with 10 cards after 8 calls.
Related
More squares, cubes and roots bingo
More math bingo
- Number bonds to 100 21 problems · 21 answers · 4x4