Why critters instead of numbers?

Sudoku looks like a math puzzle, but you never add anything up. The digits are only names, and any nine symbols work the same. So we picked critters.

This one is for the youngest players. A child who can’t read a 7 yet can still say “there’s already a frog in this row.” That sentence is the whole game. Start on a 4 by 4 board with four critters, and the same rule carries you all the way to a full 9 by 9.

A bit of real Latin square history

Long before sudoku, mathematicians played with grids where every symbol appears once in each row and column. In a paper published in 1782, Leonhard Euler asked whether 36 officers, from six regiments and of six ranks, could stand in a 6 by 6 square with each rank and each regiment once in every row and column. He couldn’t find a way, and in 1901 Gaston Tarry confirmed there isn’t one. Euler wrote his squares with Latin letters, which is why these grids are called Latin squares.

Euler wasn’t the first. The Korean mathematician Choi Seok-jeong wrote down a matching pair of 9 by 9 squares in his book Gusuryak more than 60 years earlier. Later, at Rothamsted in England, the statistician Ronald Fisher used Latin squares to lay out crop trials, so every kind of wheat got a fair share of good and poor soil. In 1929 he laid out a 5 by 5 Latin square of tree plots near Beddgelert Forest in Wales.

Sudoku is a Latin square with one extra rule for the boxes. For young children, NRICH, the maths project at the University of Cambridge, has a puzzle called Teddy Town for ages 5 to 11. Kids put colored teddies in colored houses so no row or column repeats a color. The teacher notes explain that it’s really a hunt for two Latin squares that fit together, the kind Euler was after. With six colors it has no answer, for the same reason Euler’s officers never lined up.

The five places

• Burrow, levels 1 to 20: 4 by 4 with four critters.
• Pond, levels 21 to 40: 6 by 6 with six critters.
• Meadow, levels 41 to 60: 6 by 6 with fewer critters to start.
• Woods, levels 61 to 80: the full 9 by 9 with nine critters.
• Hilltop, levels 81 to 100: 9 by 9 with the fewest starting critters.

Every puzzle has exactly one answer. Burrow, Pond and Woods puzzles can be solved one sure step at a time, with no guessing.

How to play

• Every row, every column and every box needs one of each critter.
• Tap a square, then tap a critter. Or tap a critter first, then tap squares to place it.
• Notes puts tiny critters in a square, as reminders. Undo takes back your last move.
• A soft red outline means two of the same critter share a row, column or box.
• Hint fills in one square. You get 3 per level. Use one hint or slip at most for 3 stars.
• Keyboard: 1 to 9 picks a critter, arrows move, Backspace erases.
• Sound is on to start. Tap 🔊 to mute, or 🎵 for music.
• Earn 3 stickers in this game for your QuickBOP sticker book.

Tips

Find the almost-full lines. A row with one empty square has only one answer. Say the missing critter out loud before you tap.

Follow one critter. Pick the bee and check each box. If a box has only one square where a bee is allowed, the bee goes there.

Use notes on the big boards. Jot the two or three critters that could fit a square, then come back to it.

Watch for the hop. Critters only hop when their whole row, column or box is right. If you fill a line and nobody hops, something in it belongs somewhere else.

Your turn

Four critters are waiting in the Burrow at the top of this page. Start level 1 and see how many stars you can carry up to the Hilltop.