# What you’re missing: grow your child’s math skills with logic puzzles for kids.

## Keep math exciting, and your kids will keep doing math. Hello, logic puzzles!

Logic puzzles for kids are a great way to pique your child’s interest in mathematics since logic and math go hand-in-hand. Any time kids are engrossed in tricky brain teasers, they’re building the skills they’ll eventually use to ace the SAT, lead a First Robotics Competition team to victory, and even split a restaurant check with their future roommates.

There are also more benefits from regularly engaging with puzzles. Research shows that playing brain games will develop analytical thinking skills, giving students the flexibility to use problem-solving strategies in unexpected ways. For example, in English 101, when your student needs to tie in a thesis statement to a conclusion, they’ll be calling up their logical thinking skill set. In robotics, if the sandwich-making robot they build puts the bread on the cheese (instead of the cheese on the bread), analytic thinking will allow them to debug it and eat in style.

Whether it’s a rebus problem, lateral thinking challenge, or mind-melting sudoku puzzle, each enigma makes your kid (and you) a better writer, thinker, strategist, and mathematician.

## What is logic, and why is it essential in critical thinking?

The word logic comes from the Ancient Greek word logos, originally meaning “the word” or “what is spoken.” However, over time, the term has come to mean “thought” or “reason.” A logic puzzle is, literally, a thought puzzle! The etymology explains why there are so many varieties of logic puzzles for kids — from math puzzles built solely on relationships between numbers like “24” to tricky wordplay riddles. Check these out:

What gets wetter and wetter the more it dries?

What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?

I am weightless, but you can see me. Put me in a bucket, and I’ll make it lighter. What am I?

Stumped? You’ll find the answers are at the bottom of the article.

## Wow! There are so many types of logic puzzles.

Problem-solving involves an extensive range of cognitive tools, such as inductive logic, deductive reasoning, analogy, wordplay, sequencing, and even sometimes just listening very, very carefully.

Here is a classic example of a puzzler that relies entirely on what scientists call metacognitive listening, which is just a fancy way of saying, “pay close attention to what the question is asking.”

A farmer in California owns a beautiful pear tree. He supplies the fruit to a nearby grocery store. The store owner has called the farmer to see how much fruit is available for him to purchase. The farmer knows that the main trunk has 24 branches. Each branch has exactly 12 boughs, and each bough has precisely six twigs. Since each twig bears one piece of fruit, how many plums will the farmer be able to deliver?

Wait? What! Did you do a bunch of multiplication? Here’s a clue: you don’t need to. Why? Well, it’s nice to know so much about the farmer’s beautiful pear tree, but he’s delivering plums!

Just as a customer at an ice cream shop has options, so does a logic puzzle fan. Like ice cream, challenges come in a lot of flavors, and people usually have their favorite. Let’s explore a few and see what your favorite is.

### Classic mathematical reasoning problems.

The IMACS curriculum focuses on developing mathematical reasoning skills in students, so it probably isn’t surprising that IMACS has created hundreds of unique logic problems. Try this one from the IMACS library:

It was a frosty winter evening when sisters Aurora, Elizabeth, Minnie, and Rorona were sitting by the fireplace drinking hot cocoa. As they were playing and drinking from their cups, one of the sisters accidentally spilled her cocoa onto the carpet. Their mother checked on her daughters soon after and asked as she picked up the cup, “Who spilled the cocoa?” Only one of the sisters told the truth.

Elizabeth said, “The cup belongs to Rorona.”

Rorona said, “The cup belongs to the sister whose name contains letters that can make up the word ‘roar.’”

Aurora said, “The cup belongs to the sister with two o’s in her name.”

Minnie just stared at the cocoa on the floor.

Who was the perpetrator of the spilled cocoa?

This type of logic problem can be extremely challenging before you’ve grown your reasoning skills. But in many ways, it is a bite-sized thinking hurdle that, on a small-scale, mimics the complexities inventors, engineers, and technologists face in real life: it requires an understanding of intertwined relationships and the ability to deploy deductive reasoning. Any challenging puzzle will improve a person’s mental flexibility, but logical reasoning is the most important to develop as it underpins many other essential problem-solving strategies.

Fortunately, logical reasoning is learned, not innate. The IMACS program is specifically designed to develop the thinking skills these more challenging problems require. In fact, IMACS even offers fun and engaging classes devoted to logic puzzles each summer for kids in first through eighth grade.

Looking for the answer to the problem of the spilled cocoa? You can find it (and others) at the end of the article. Please don’t get frustrated if these problems are tricky! Keep in mind that mathematical reasoning has a lot in common with learning a language:

• it’s best and easiest to master when you are young;
• you have to put the time in to get fluent;
• once you are fluent, the skill is so automatic it feels as if you’ve always known how to do it!

Want to try another one? Great! Give this a shot:

Lori, Matt, and Nancy each ordered a sandwich, a side, and a drink at a fast-food restaurant. When their orders were delivered: Lori received a fish sandwich, french fries, and water. Matt received a chicken sandwich, onion rings, and root beer. Nancy received a veggie sandwich, potato chips, and lemonade.

Unfortunately, the orders were not delivered properly.

Lori said, “Only one of these is correct – and it’s definitely not the water.”

Matt said, “And only one of my items is correct!”

Nancy said, “Only one of my items is wrong.”

One employee said, “I know that the chicken sandwich goes with the water.”

Another employee said, “I know that the potato chips go with the root beer, but not with the fish sandwich.”

Help the manager sort this out! Every statement is accurate. Who ordered what?

The fast food mix-up problem is tough! Using paper and pencil can be a great help. Don’t give up. The solution is at the end of the article.

### Brain Teasers.

Another category of logic problem is the classic “brain teaser.” Brain teasers are often tricky because they rely upon a skill called “lateral thinking.” The lateral thinking problems challenge you to reexamine your assumptions about the question. Here is a classic lateral thinking puzzle:

8,549,176,320

Spoiler alert! We’re about to reveal the answer. Take a look for a minute and see if you can figure it out first. If you are stuck, take a look at the clues before going right for the solution!

Clue #1: You probably noticed every digit (0 through 9) is represented. Nice! And you know this is a lateral thinking problem (because that’s what this section is about!) In lateral thinking problems, the solution lies in thinking beyond the assumptions you bring to the problem.

Because this logic problem presents you with numbers, you probably think you should use your math skills to find a solution. In other words, once your brain sees the numbers, it quickly assumes, “Aha! Look for numerical relationships between the numbers!”

The essence of lateral thinking problems is that the solution will remain elusive as long as you stay locked into presuppositions you bring with you. So, is there another way to think about the math puzzle you are seeing?

Clue #2: What if you had to write this number out in words?

Clue #3: What is the relationship between the first letter of each word you wrote out in the previous clue?

Did you get it? Awesome! It’s all the digits, written as words, arranged in alphabetical order.

### Can you solve the riddle of thirty cents?

Some people get upset when they find out the solution to a lateral thinking problem. It is frustrating when our mental shortcuts that are usually helpful become the source of our failures. Yet, when people are particularly adept at thinking beyond these frameworks’ constraints, they often become inventive entrepreneurs and entrepreneurial inventors. They develop the ability to think outside the box and the power to create disruptive innovations.

Now that you know that this section is all about lateral thinking and questioning your presuppositions, see if you can solve the next one yourself. You can start by asking, “What assumptions am I making that are likely to be turned upside down by the words of this question?” Let’s give it a try!

In my hand, I have precisely two American coins. Together, they add up to thirty cents. One of them isn’t a nickel. What are they?

Seems impossible, right? A lateral thinking problem’s benefit is realizing that many assumptions about “impossibilities” are just a function of our own limiting beliefs. If you can reframe a problem in a new way, what was once considered “impossible” suddenly becomes trivial!

Give up? Want the answer? We did say there were two coins, and indeed, one of them is not a nickel. That one– that isn’t a nickel– is a quarter. But the other one? Yes, it’s a nickel.

### The mystery of the two brothers. Impossible?

On this one, see if you can break down your assumptions to find the answer.

A woman had two sons. They were born at the same hour on the same day of the same month in the same year. However, they were not twins. How is this possible?

While some people dismiss lateral thinking puzzles as not “real logic puzzles,” they have tremendous value in teaching kids (and adults) the difference between thinking and what scientists call “metacognitive thinking.”

In a typical logic puzzle, our work is to think. But with lateral reasoning, our work is to think about thinking. When the question proposes that the sons aren’t twins, we get locked into thinking entirely about twins.

It is that “locked-in thinking” that prevents us from seeing that two boys born from the same mother at the same time are conventionally called twins-when there are only two. But what if three brothers had been born at the same time? Everything in the problem is true, but we wouldn’t call these boys twins; we’d call them triplets!

A hallmark of lateral problems: they always seem “impossible” given the information. However, what’s impossible is maintaining logical cohesion between our assumptions and the question’s simple facts.

### If you love the feeling of your mind getting twisted in knots, self-referential problems might be your favorite kind of logic puzzle.

Self-referential puzzles, sometimes called recursive problems, are problems that will give you a feeling of your brain twisting around in knots. In these problems, the questions refer to the questions which refer to the questions… You get it. These are tough. Let’s look at a cool one created by software engineer and part-time puzzle maker Lauri Tervonen:

1. What is the answer to the second question?

A. A

B. B

C. C

D. D

2. How many correct answers in this test are B?

A. 0

B. 1

C. 2

D. 3

3. Is there a question with the correct answer A?

A. No

B. Yes, 1

C. Yes, 2

D. Yes, all 3

### Stump your teachers with this fun self-referential puzzle.

If you liked that one, here is one of the shortest versions of a self-referential problem. This one is great because it is easy enough to remember. You can try to stump your teachers and relatives!

Guess the next three letters in the series GTNTL.

You might have realized the answer to this one instantly, but if you haven’t yet, don’t give up too quickly! Another reason to work on puzzles is to get better at perseverance.

Still stuck? Here’s a hint: this section is about self-referential puzzles!

Did you get it with that last hint? The next three letters in the sequence are: “I, T, S.” which are the starting letters of the words “in the series.” The initial letters of the words in the problem are: G for guess, T for the, N for next, and so on, creating the sequence: G.T.N.T.L.I.T.S…

If you like these examples and recursion is interesting to you, check out this great article on recursion, language, and logic.

### Are there other types? Yes! Logic Grid Puzzles, Kakuro puzzles, a Sudoku puzzle, Rebus, Hitori, Hanjie, Nurikabe, Slitherlink, Futoshiki, crossword puzzles, Magic square, Mechanical, Cryptos. And that’s just a start.

Wow. That’s a lot of different kinds, and that doesn’t even cover everything! Companies and law schools even use logic puzzles for job hiring and admissions because they can reveal cognitive strengths.

If you find logic grid puzzles fun and you learn how to do them well, getting into a top law school will be a lot easier. On the LSAT, the law school admissions exam, logic grid puzzles make up 23% of your score! Here is a fascinating article about the brain teasers top tech companies ask in their interviews.

The best way to get good at puzzles is to do them! And what’s the easiest way to do that? If you want your kids to get a steady stream of logic time, link it to other habits you already have.

Do you always eat dinner together after sports practice on Tuesday night?

Try picking up this fantastic source of problems, “The Moscow Puzzles: 359 Mathematical Recreations” and do one of the questions over dinner each week. Whoever figures it out first doesn’t have to do the dishes!

Here’s another example of using habit linking to work on logic problems consistently. Do you and your child read books together each night? A night or two a week, add in an easy logical reasoning riddle before you read!

Time in the car is another excellent time to figure out a challenging puzzle. Where you do them matters less than being consistent. The best way to be consistent is to make brain games a part of an activity that is already happening regularly. This technique, called habit-stacking, can be used for building any healthy habit. In just a few months, you’ll see your child’s problem-solving ability grow. Within a season, you’ll see your child’s improved analytic skills positively affecting their math abilities and love for the subject.

### Board games and puzzles for raising analytic thinkers.

Logic puzzles can take many forms. Even the famous Rubik’s Cube is a logic puzzle. It is in the category of “mechanical puzzles.” Activities like the Rubik’s cube and board games are a great way to encourage and build analytic thinking while simultaneously having a great time! A board game like Splendor, which relies on making trades and judging the value of relative items, is excellent for sharpening analytic thinking skills.

If you want a genuine puzzle rather than a competitive board game, check out the ThinkFun line of puzzles or Puzzle Baron’s Logic Grid Puzzles. The IMACS curriculum is also excellent at building these skills. In fact, one of ThinkFun’s puzzle designers is an alumnus of IMACS. You can read Mark Engelberg’s story to learn more about how he developed the great puzzle, Chocolate Fix. If you want to see how the IMACS program can make your child a future puzzle designer, inventor, entrepreneur, or excellent all-around thinker, bring your child (virtually!) to our free assessment class. We’ll play math games with them for about thirty minutes and give you a free placement analysis, so you’ll know how you can best help your child level up their mathematical reasoning skills.

### Putting it all together. Five reasons to start doing logic puzzles with your kids.

1. Logic problems teach kids different approaches to problem-solving. Techniques like elimination, working backward, “thinking outside the box,” and critical thinking skills are all approaches that get a workout and are improved.
2. Active brains grow. If the brain is like a muscle, math puzzles are barbells. Work out your brain often to keep in shape and get powerful.
3. Interesting math—the kind of math engineers, inventors, and mathematicians do— is a lot more exciting than counting by rote and applying some equations to a set of numbers. In many ways, logic puzzles are just as important as “school math” in rounding out the skillset your kids will need in the future.
4. Sometimes gifted kids learn to dread math. Sometimes kids who are struggling in the subject tune out because they think it is boring. However, often this is because their only exposure has been memorizing a formula or completing a worksheet. Puzzles are a great way to help kids who are disengaging in school to see how beautiful and exciting math is.
5. Logic puzzles are word problems in disguise. “No! Not the dreaded word problem,” a lot of kids moan when they see a wall of text in their math book. But succeeding at math requires reading comprehension skills. Brain teasers mostly come in the form of a word problem, so kids learn to enjoy the format rather than be intimidated by it.

## The big, fantastic secret to make your kids fall in love with logic puzzles.

Sometimes it’s hard to get your kids excited about something that isn’t on a screen. We get it; we’re parents too. But in thirty years of teaching logical reasoning skills to kids, we’ve figured out one sure-fire trick to get kids fired up about working hard on tricky problems: tell them the answer.

Hey! Don’t push the back button yet! Here’s how giving them the answer helps get them excited. Get a few logic puzzles; a great source is the NPR show “Car Talk” that ends every episode with a brilliant head-scratcher. Let your child show you the problem. Flip the script! Let them watch you struggle with it, work on it, and most importantly, have fun with it. These puzzles are fun– but ham it up anyway. When you try another one (maybe a few days or a week later), insist that you get to try it first. Week three, say that you want to try first, but you are willing to let them go first.

By modeling how much fun it is to do the puzzles, you give them a reason to want to try. This is a principle that works in our classes too. Our teachers have so much fun teaching math to IMACS’ students that kids are excited to learn. If you haven’t seen one of our classes yet, you can learn more about kids who have taken them; if you want to see our classes yourself, sign up for a free trial.

## Thanks for reading! Here is one more fun problem for you.

Peter’s father has five sons. The names of four sons are Fefe, Fifi, Fafa, and Fufu, respectively. What is the name of the fifth son?

## If you liked these, you’re going to love IMACS. Try a free placement class and see how much fun mathematical reasoning is.

### Wordplay riddles:

What gets wetter? A towel.

What can run? A river

I am weightless? A hole

### The case of the spilled cocoa:

Solution: Aurora

Explanation:

Statements 1 (by Elizabeth) and 3 (by Aurora) are essentially saying the same thing. Both of these statements can’t be true, so both Elizabeth and Aurora must be lying. Therefore, Rorona must be the one telling the truth. Since we know that Rorona is not the one who spilled the cocoa, it must be Aurora since she is the only sister besides Rorona whose name has letters that can make ‘roar.’

### The case of the fast food fiasco:

Solution:

Lori ordered a fish sandwich, onion rings, and lemonade.​

Matt ordered a chicken sandwich, french fries, and water.​

Nancy ordered a veggie sandwich, potato chips, and root beer.

Explanation:

Since the potato chips go with the root beer, either Nancy’s side is wrong or her drink is wrong. So, her veggie sandwich is correct. Lori did not get the chicken sandwich (because it goes with the water, which she did not get.) It follows that:

Lori ordered a fish sandwich, ________, and ________.

Matt ordered a chicken sandwich, ________, and water.

Nancy ordered a veggie sandwich, ________, and ________.

Since only one of Matt’s items was correct, he did not get the onion rings. Since the chips go with the root beer, Matt did not get the chips. So, he got the fries.

1. (A)
2. (A)
3. (C)