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 Question from Kenya, a parent: my number is less than 25 my number of tiles will make only one rectangle my number is odd my number is a factor of 36

Hi Kenya,

There is no formal procedure or set of steps to solve problems like this, you just follow the clues that ar in the statements.

Statements 1 and 3 are straightforward, the number is odd and less than 25.

For statement 4 I would look at the prime factorization of $36.$ $36 = 2 \times 2 \times 3 \times 3.$ Thus the odd factors of $36$ are $3, 9$ and $1.$

Statement 2 is about arrays. From 9 tiles you can make 2 arrays, one 9 by 1 and the other 3 by 3. Thus 9 doesn't satisfy the condition in statement 1. From 3 tiles you can only make 1 array so 3 satisfies the conditions in all four statements. I expect that 3 is the answer expected to this problem although I would argue that 1 also satisfies all three conditions.

Now try the other problems you sent us and, if you get stuck, write back to say what you have done and where you are stuck.

Penny

Kenya wrote back

Ok, I tried this puzzle the following way and came up with 120 and 240 left over but don't know which is the answer-help:
my number has three digits
my number is less than 300
my number is a multiple of 40
my number is a multiple of 60

My process was write the multiples of both 40 and 60 that are under 300. Now, 120 and 240 are both multiples of 40 and 60 so which is the answer. My theory is since it has to be a three digit number when I divide both 40 and 60 my 120 it gives me 3 and 2 respectively which tells me that there are 3 or fewer numbers in the answer because when I divide 40 and 60 by 240 I get 6 and 4 respectively which would be too many numbers for the answer. What do you think?

Also, there is another one that has my head spinning:
my number of tiles will make a rectangle 4 tiles wide
my number of tiles will make a rectangle 2 tiles wide
my number of tiles will make a rectangle 5 tiles wide
my number is less than 50?

For the second problem you are looking for a number that is a multiple of 2, a multiple of 4 and a multiple of 5. $2 \times 5 = 10$ is a multiple of $2$ and $5$ but not $4. \; 4 \times 5 = 20$ is a multiple of 2, 4 and 5 so $20$ is a correct answer. Is there another correct answer?