Ages 6–8 · 8 little discoveries
Piko’s Logic Lab
Eight discoveries with two-clue sorting, repeating and growing patterns, order clues, ruling things out, a picture table, arrow commands and fixing a mistake.
- Learn
- Play
- Show
Choose a lesson. You can revisit any discovery.
Read the lessons
Sort with two clues
Sort cards into boxes that need two features together, a shape and a colour.
Piko has four boxes. Each box needs two clues: a shape and a colour. The first box is for yellow, dotted circles. The other boxes use a different shape or a different colour.
This yellow, dotted triangle does not fit the yellow circle box. Its colour fits, but its shape does not. A card must fit both clues.
A turquoise, striped triangle goes in the turquoise triangle box. First check its shape, then check its colour. Each card has only one box.
Now you try. Choose a card, then touch its box. Ask two questions: which shape, which colour? You can move a card again.
A group that repeats
Continue a pattern whose repeating group has three cards: two the same and one different.
Look at Piko’s trail: star, star, leaf. Then star, star, leaf again. A group of three repeats. We can call it A, A, B: two the same, then one different.
This trail repeats another group: leaf, apple, apple. That is A, B, B: one card, then two the same. Find where the group starts again.
Be careful. Star, star, leaf, then star, leaf, leaf. The second group is not the same, so the pattern breaks. The same group must come back in the same order.
Now you try. Say the group out loud: acorn, acorn, apple. Then find which part of the group comes next. Choose a picture, then touch an empty place.
Patterns that grow
Find how many blocks a growing pattern adds each step and use it to continue the pattern.
Piko builds towers. The first has one block, the second has two, the third has three. Each step adds one block. A growing pattern adds the same amount every time.
This pattern grows faster: two blocks, four blocks, six blocks. Count what is added between towers: two blocks each time. The next tower would have eight.
This row is different: one, two, four. First one block was added, then two. The amount changed, so it does not grow by the same amount each time.
Now you try. Find the step first: from three blocks to four blocks adds one. Then add the same amount again to keep going.
Order clues
Put three or four cards in order using clues such as first, last, right after and between.
Three cards stand in a line. The first clue says: the star is first. First means place 1, at the very start of the line.
The next clue says: the apple is right after the star. Right after means the very next place. So the apple is in place 2.
Look at this line. The apple is after the star, but the leaf is in between. That is not right after, so this line does not fit the clue.
Start with the clue that gives an exact place. Place the other cards one clue at a time. At the end, read every clue again to check.
Rule things out
Use “it is not…” clues to rule out cards that cannot match, then name the card that is left.
Piko hides one card. Clue 1: it is not a circle. So no circle can be the hidden card. Both circles are ruled out.
Two cards are left. Clue 2: it is not turquoise. A turquoise, striped card cannot be the hidden one. The triangle is ruled out too.
One card is left: the purple, crossed square. It is not a circle and not turquoise. It breaks no clue, so it is the hidden card.
Rule out only cards that break a clue. A card that fits every clue stays in. Now you try: touch each card that cannot be the hidden card.
A table with one empty cell
Complete a 4 × 4 picture table with one empty cell so that every row and every column has each picture once.
Piko’s table has four rows and four columns. Each row has all four pictures, once each. Each column does too. One cell is empty.
Look along the empty cell’s row. It has a square, a star and a triangle. There is no circle, so the circle is missing from this row.
Check the column too. It also has a square, a star and a triangle. The circle is missing here as well. So the circle fits the empty cell.
What if we put a triangle there? Then the row and the column would each have two triangles. A picture can appear only once in a row or a column. Now you try: check the row, then the column.
Arrow commands
Follow a list of arrow commands one square at a time, and write the commands for a walk.
The board has nine squares, numbered 1 to 9. Piko starts on square 1. A command is an arrow, and one arrow means one square. Right, then down: Piko goes to square 2, then to square 5.
Commands run in order. Right, right, down takes Piko from square 1 to square 2, then 3, then 6. The squares he visits are marked.
Each arrow starts where Piko stands now. Right, right does not mean square 2 twice. It means square 2, then square 3. Never start every arrow from square 1.
To write commands for a walk, compare each square with the next one. From square 1 to square 2 is one step right. Choose one arrow for every move.
Fix the wrong command
Find the one wrong arrow in a command list and replace it so that Piko reaches the star.
Piko starts on square 1 and wants the star on square 9. His plan: right, right, down, left. Follow it: squares 1, 2, 3, 6, then 5. He did not reach square 9, so one command is wrong.
To find the mistake, check one step at a time. After step 3, Piko is on square 6, right above the star. Step 4 should go down, but it goes left. Step 4 is the wrong one.
Change only the wrong step. Step 4 becomes down. Now the plan is right, right, down, down, and Piko walks 1, 2, 3, 6, 9. He reaches the star!
Do not change steps that were fine. If step 3 became left, Piko would walk back to square 2 and stop on square 5, not on the star. Change one arrow, then test the whole plan from the start.