This guideline is designed for students of different reading levels eager to participate in the Bangladesh Mathematical Olympiad, from beginners to advanced. The books are roughly arranged from easier to more challenging. You don’t have to read all of them, just pick any one you like and you can start reading. If a book feels too difficult or the language doesn’t feel right for you, don’t worry—it’s okay to move on to another one that suits you better. Above all, reading should be fun, so keep reading and enjoy your journey.
“A census-taker knocks on a door, and asks the woman inside how many children she has and how old they are.
"I have three daughters, their ages are whole numbers, and the product of their ages is 36," says the mother.
"That's not enough information," responds the census-taker.
"If I told you the sum of their ages, you still wouldn’t be able to determine their ages," says the mother again.
"I wish you'd tell me something more," replies the census-taker.
"Okay, my oldest daughter Annie likes dogs."
What are the ages of the three daughters?”
The first step is to keep a clear mind and extract any piece of information you can get. Pay attention to each sentence. The first pieces of crucial information are in the following sentence:
"I have three daughters, their ages are whole numbers, and the product of their ages is 36," says the mother.
Right now, they’re given in a non-mathematical format, but it’s easier to work with mathematical language. To convert, let x, y and z represent the ages of the three daughters. We immediately get that x, y and z are positive whole numbers (age can’t be negative), and xyz = 36. The next pieces of information are:
"If I told you the sum of their ages, you still wouldn’t be able to determine their ages," says the mother again.
"Okay, my oldest daughter Annie likes dogs."
Currently, it’s hard to understand what information they give us, but what we do understand is that the sum of their ages is somehow important in this problem. Finding no other strategy, let’s make a table, consisting of all possible values of x, y and z (knowing that they are positive integers with a product of 36 is enough to determine all possible values), and their sums.
| (x,y,z) | (1,1,36) | (1,2,18) | (1,3,12) | (1,4,9) | (1,6,6) | (2,2,9) | (2,3,6) | (3,3,4) |
|---|---|---|---|---|---|---|---|---|
| x+y+z | 38 | 21 | 16 | 14 | 13 | 13 | 11 | 10 |
Now, pondering the third info given makes sense: if the sum of their ages were 13, then the census-taker wouldn’t be able to determine their ages, since there are 2 possible options! We’ve narrowed the ages down to two options now: (1,6,6) and (2,2,9).
The final information given seems unrelated to mathematics at all, so we should pay close attention to its implications. Note that the statement “My oldest daughter Annie likes dogs” implies that she has an oldest daughter i.e only one daughter is the oldest. This means that their ages can’t be 1, 6 and 6 years! Thus, their ages must be 2, 2 and 9 years, and the problem is solved.
To get better, focus MORE on solving problems, not just reading books. A fundamental part of training is learning various problem solving techniques and applying them on later problems. This is done by frequent problem solving. Practice regularly and try harder problems as you improve. Just reading won’t help you develop your skills—you need to solve more and more problems!
"Never give up! Struggling with a problem doesn't mean you're not capable. Keep pushing forward with confidence and patience. The more you practice, starting with easier challenges and gradually tackling harder ones, the more you'll sharpen your skills. Over time, you'll be amazed at how you can solve even the most difficult problems!
Remember, practice makes progress! You can do it!"