Cryptogram Math Puzzles for Elementary Students: How to Solve Them
- Vasudha Uddavan
- Jan 10, 2019
- 4 min read
Updated: 2 days ago
Cryptogram puzzles are one of my favourite math enrichment activities. They help children develop logical reasoning, arithmetic fluency, and problem-solving skills while feeling more like a puzzle (fun) than a worksheet.
What is a Cryptogram/ Cryptarithm?
A Cryptogram/ Cryptarithm is a puzzle where letters and symbols are used in place of numbers. Our goal is to figure out which number each letter and symbol corresponds to.
Rules:
Different letters represent different digits.
Same letters represent the same digits.
The leading digit represented by a letter can never be 0. For eg, if I have BAT, B can not be zero
Are Cryptarithms used in math competitions?
These are very popular in mathematical competitions, especially in MOEMS (Math Olympiads for Elementary and Middle Schools) and CML (Continental Math League). In fact, CML competition gives cryptograms to kids as young as second grade.
Cryptarithm puzzles are also engrossing and interesting to solve. They give our brain a good workout.
I also do these puzzles with my 5-year old kid and my students (as a part of my Math Enrichment program) and they enjoy it. The puzzle given above has been one of my more popular puzzles because I posted it around Halloween with the word BOO :) And it's easy to solve.
What age are cryptarithm puzzles suitable for?
They are great for all ages—from elementary students to adults. The puzzles can easily be adapted to different skill levels.
In this blog, I've focused only on addition ones, and hence they are suitable for Elementary students.
Now, let's look at various cryptogram puzzles and how to solve them
Let us start with the most basic one.
As I said, each letter stands for a single-digit number, and different letters represent different numbers.
Cryptogram Puzzle 1: For kids in grades 1-2
So here we have
5+B=; 5+1=6 hence B=1
A+3=7; 4+3=7 hence A=4
45+31=76, and that verifies our answer
So our solution is A=4; B=1
Cryptogram Puzzle 2: For kids in grades 1-2
Here, we introduce the idea of carryovers
It's given that 8+B=7; but 8 plus B (a single digit whole number) cannot equal 7 and hence it must 8+B should be equal to 17; and the 1 would be carried over.
So, 8+B=17; 8+9=17; hence B=9
Now we have a carryover of 1 in the ten's place
So, 1+A+2=6; A+3=6; 3+3=6; hence A=3
We know that 38+29=67, and hence our solution is correct
So we have A=3 and B=9
Cryptogram Puzzle 3: For kids in grades 2-3
A+C=9; It could be any possible answer ranging from 0+9=9 to 4+5=9. So how do we narrow it? There's an A in the hundreds' place in the sum. A's value has to be the same in both places. So let's see if we can figure out the A in the hundreds' place
When 2 2-digit numbers are added, the greatest carry over you can have in the hundreds' place is 1.
eg, let's take the worst case and add 99+99 = 198.
So A has to be 1.
The other way to look at it is 6+B=0 can have a greatest carryover of 1. When 2 single digit numbers are added (the highest being 9+9=18), you can only have a carryover of 1. Hence A=1
Now that we know A=1; rewrite your problem as 61+BC=109
Now we have 1+C=9; 1+8=9; hence C=8
We also have 6+B=10; 6+4=10; hence B=4
61+48=109, it works, and our solution is correct
Solution: A=1; B=4; C=8
Cryptogram Puzzle 4: For kids in grades 3-5
Pretty similar to Puzzle 3. Figuring out B is easy because B is in the hundreds' digit, and it can only be 1.
Pitfall to watch out for: It is tempting to say that A=4 because 4+4=8.
But then, if A=4, the tens column would not be correct. 4+0 cannot be 0. So there needs to be a carryover. Hence, A+A should be equal to 18. Hence A=9
99+9=108; So our solution is A=9; B=1
Cryptogram Puzzle 5: For kids in grades 3-5
A+A+A = 4; which means 3A=4; since 3*A cannot be equal to 4, it has to be equal to 14 or 24. (When 3 single-digit numbers are added, the greatest carry over is 2; eg, 9+9+9=27)
3*8=24; Hence A=8
We have a carryover of 2; so 2+2+3=B; and B=7
28+38+8=74, and it works
So our solution is A=8 and B=7
Now it's your turn to try. Try these problems and write the answers in the comments section below
Like these Cryptograms? You can find a lot more of these if you follow my Facebook or Pinterest page.
P.S. I just started Cryptograms with my 5-year-old son yesterday, and this will give you an idea of how to start with your own child.
I made up all these problems for him. I always handwrite the problems one-by-one for him, as young kids tend to get distracted when they see too many problems to solve.
You can also see how I started from an extremely easy problem of A+5=8 and moved on to 2-digit addition with carryovers. We also later did 2-digit addition with carryovers in the tens and hundreds place.
This is also a good way to practice addition and subtraction. Kids love the variety.
To see more Cryptogram puzzles, click here
Cryptogram puzzles are a fun and effective way to build arithmetic fluency, logical reasoning, and problem-solving skills. Start with simple one-digit puzzles and gradually introduce carryovers and multiple variables as students gain confidence. Whether you're a parent, teacher, or math enthusiast, these puzzles provide an engaging alternative to traditional worksheets.
About the Author:
I am Vasudha, an Online Math Tutor. I do Math Enrichment classes for Elementary and Middle School students. I specialize in the Beast Academy and AoPS curriculum and have been teaching it for more than 10 years. I will also be running Online Math Enrichment Programs during the summer.
Did you enjoy these puzzles? Have a friend or a family member who'll benefit from these as well? Please do share the blog :)
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