By eight or nine, many children can read a puzzle of a few sentences by themselves, know most of their times tables, and start to enjoy problems that "take some thinking". This is where word puzzles really pay off: your child has to read carefully, hold several conditions in mind, and then prove to themselves that their answer is right. Every child moves at their own pace, so treat these ages as a rough guide.
Below are twelve puzzles in three groups: numbers, line-ups and shapes. Let your child read each one on their own, and only offer the hint when they ask for it. Before they look at the solutions at the end, invite them to try the self-checking tips in the fourth section.
Secret numbers and word problems
| Puzzle | The question | Hint if your child is stuck |
|---|---|---|
| 1 | I am a two-digit number. My tens digit is double my ones digit. My two digits add up to 9. What number am I? | Try a ones digit of 1, 2, 3… and work out the tens digit each time |
| 2 | I am bigger than 30 and smaller than 40. I can be divided by 4 with nothing left over, but not by 3. What number am I? | Write 31 to 39 and cross out the numbers that break each rule |
| 3 | A brother and sister's ages add up to 15. The brother is 3 years older. How old is each of them? | If the brother were 3 years younger, they would be the same age |
| 4 | There are chickens and dogs in the yard. You can count 5 heads and 14 legs. How many chickens and how many dogs are there? | Draw 5 animals and give every one of them 2 legs first |
Line-ups with conditions
| Puzzle | The question | Hint if your child is stuck |
|---|---|---|
| 5 | A bear, a rabbit, a dog and a cat stand in a line. The bear is at the front. The rabbit is not at the front or the back. The dog is right in front of the cat. What is the order? | Draw four boxes, put the bear in first, then try the rabbit in each space that is left |
| 6 | Five books, red, blue, yellow, purple and orange, stand on a shelf from left to right. The yellow book is in the middle. The red book is right next to it on the left. The blue book is at the far right. The purple book is not next to the red book. What is the order? | Fill in the three clues you are sure of first, then decide about the purple book |
| 7 | A cat, a dog and a rabbit each like one activity: swimming, drawing or football. The cat does not like swimming. The dog does not like drawing or swimming. Who likes what? | Draw a three-by-three table and put a cross in every "no" box |
Counting shapes and crossing bridges
| Puzzle | The question | Hint if your child is stuck |
|---|---|---|
| 8 | Draw a square split into a two-by-two grid. How many squares are there? | The big square around all four counts too |
| 9 | Draw a three-by-three grid. How many squares are there? | Count each size separately: one box, four boxes, nine boxes |
| 10 | Draw a strip of three boxes in a row. How many rectangles are there (squares count too)? | Count the ones that are one box, two boxes and three boxes long |
| 11 | A river has an island in the middle. The top bank has 2 bridges to the island, the bottom bank has 2 bridges to the island, and 1 long bridge goes straight from bank to bank. Can you cross every bridge exactly once? Where do you start? | Count how many bridges each piece of land has |
| 12 | Draw four pieces of land, each joined to all three others by one bridge (six bridges in total). Can you cross every bridge exactly once? | Use the counting trick from puzzle 11 |
Puzzles 11 and 12 hide a neat rule: every time you walk onto a piece of land in the middle of your route, you need another bridge to walk off it again, so it must have an even number of bridges. Only the start and the finish can have an odd number. Let your child discover the rule through the two puzzles rather than telling them first.
Tips for checking the answer
At this age, children often want to know straight away whether they are right. Before they peek at the solutions, invite them to check their own answer in one of these ways:
- Put the answer back into the question. Is the answer to puzzle 3 "the sister is 6 and the brother is 9"? Do the ages add up to 15, and is the brother 3 years older? If both are true, the answer is safe.
- Walk through every clue. For a line-up, reread each sentence of the puzzle and point at the line your child made: is this clue true? One clue that does not fit means it is time to rearrange.
- Ask "Is there another way?" A good puzzle has only one answer. If your child finds two orders that both work, they may have missed a clue.
- Count in order. For shape counting, write down how many squares of each size on separate lines, so nothing gets counted twice or missed.
If your child's answer is different from the solution, do not just cross it out. Look together for the step where the two ways of thinking split; often it is just a "not" that got skipped.
In Dologi, the "Who lives where?" and "One stroke" puzzles in the Logic topic use these same two kinds of reasoning: putting clues together to work out who is where, and finding a route along every line without going over any of them twice.
Answers and step-by-step solutions
- 63. A ones digit of 1 gives a tens digit of 2, which adds up to 3. A ones digit of 2 gives 4, which adds up to 6. A ones digit of 3 gives 6, which adds up to 9: that is the one.
- 32. Between 31 and 39, the numbers you can divide by 4 are 32 and 36. 36 can also be divided by 3, so the answer is 32.
- The sister is 6 and the brother is 9. Take 3 years off the brother and the total is 12, with both the same age, so 6 each. The sister is 6, and the brother is 3 more, which is 9.
- 3 chickens and 2 dogs. Give all 5 animals 2 legs and you have 10 legs, so 4 legs are missing. Each dog needs 2 more legs, so there are 2 dogs and 3 chickens. Check: 3 × 2 + 2 × 4 = 6 + 8 = 14.
- Bear, rabbit, dog, cat. The bear is in place 1. If the rabbit were in place 3, places 2 and 4 would not be next to each other, so the dog could not be right in front of the cat. So the rabbit is in place 2, the dog in place 3 and the cat in place 4.
- Orange, red, yellow, purple, blue. Yellow is in place 3, red in place 2 and blue in place 5. That leaves places 1 and 4. Place 1 is next to the red book, so purple goes in place 4 and orange in place 1.
- The dog likes football, the cat likes drawing and the rabbit likes swimming. The dog does not draw or swim, so the dog plays football. The cat does not swim, and football is taken, so the cat draws. That leaves swimming for the rabbit.
- 5 squares. Four small squares and one big one.
- 14 squares. Nine one-box squares, four two-by-two squares and one three-by-three square: 9 + 4 + 1 = 14.
- 6 rectangles. Three that are one box long, two that are two boxes long and one that is three boxes long: 3 + 2 + 1 = 6.
- Yes, but you must start on one bank and finish on the other. Each bank has 3 bridges (odd) and the island has 4 (even). One route: top bank to the island, back to the top bank over the second bridge, across the long bridge to the bottom bank, bottom bank to the island, and back to the bottom bank.
- No. All four pieces of land have 3 bridges, so there are four places with an odd number. A route has only one start and one finish, so at most two places can have an odd number of bridges.
In short
- Eight- and nine-year-olds are ready for word puzzles: reading the question alone, juggling several conditions, and proving their own answer.
- Good hints show a way to begin (try each option, draw boxes, make a table) without giving the answer away.
- Teach your child to check before peeking: put the answer back into the question, walk through every clue, ask "Is there another way?".
- A wrong answer is a chance to find where two ways of thinking split, not something to cross out.
Read more: One-stroke drawing puzzles: tracing every line without lifting the pencil