One of Daegan’s favourite sort of question for our ‘Problem of the Day’ is what I call a “What Number Am I?’” riddle. Here’s some that we’ve done in the past few weeks:
All three of my digits are the same. The sum of my digits is 6.
I am a 2-digit even number. I am less than 30. The product of my digits is 12.
I have 3 different digits, all of them odd. Digits are in order from least to greatest. I am evenly divisible by 5.
Daegan also did some hundred board “What Number Am I?” logic problems, in which he needed to eliminate possibilities from the board until he was left with the only (and correct) answer. Here’s two of them, that we got off this site:
So why do both Daegan and I enjoy these sorts of questions? Aside from the obvious (we LOVE riddles and logic here), I think it is because these riddles are a fun way to learn and practice “the language of math.” In order to solve the above riddles, one needs a solid understanding of ‘math language words’ like sum, digit, even, less than, product, etc. as well as familiarity with math concepts that form part of our ‘common knowledge’ in our culture: How many pennies in a dollar? Days in a month? etc.
There is an element of creativity to this as well when Daegan creates a problem for me to solve. I begin by having him write a number on a small piece of paper on the table where I cannot see it (so he can refer to it easily), and to think of some ‘clues’ about that number. For example, he wrote this riddle on the board for me after solving the second riddle (“I am a 2-digit even number…”) above:
I am a 2-digit even number. I am less than 100. My digits add to 12.
“How interesting!” I replied. “There’s actually several answers. 48, 66, and 84. You’ll have to make another clue for me so I can solve this riddle.” Daegan was a bit stumped at first, as in the model question 3 clue statements were sufficient information to solve the riddle. So we started talking about other math concepts and terms: greater than and less than, fractions and ratios, prime numbers, etc. He then created this additional clue for me:
My units digit [i.e., ones digit] is half my tens digit.
And I was now able to give him his answer: 84. I offered a few other possible clues he could have used: my digits are not identical; my tens digit is larger than (or double) my units digit; if you add my units digit to itself, you get my tens digit, etc. Daegan thought is was interesting how many ways you could give information in math—even identical information. (e.g., A is half of B means the same as B is double A, or B+B = A).
Have fun with “What Number Am I?” problems, and if you or your kids create some fun ones, please share! I should add that these were also among my class favourites when I taught grade 5/6, especially creating their own riddle for a classmate to solve. We made them in little lift-the-flap books (think typical birthday card shape turned sideways), with the clues on the front, and the solution and the working out of the clues on the inside (lift the flap to see the answer). Some kids got very into decorating them with math symbols, shapes, terminology to boot! We put them up on the bulletin board (wall) for parent-teacher conference night, and it was quite fun watching “math anxiety’” stricken parents learn that their child created this riddle, AND could teach them (the parent) how to solve it!