Exponents and order of operations

Question

Use the numbers 1,2,4 and 5 in any order to write expressions to equal each integer from 1 to 20

Answer 1

It sounds like for each number 1 through 20, you need to use all four numbers (1,2,4,5) combined with some collection of operations (+,-,*,/,^). There's no difficult "trick" to this thankfully - to answer this question, you basically need to ask yourself: "How do I get this number?". I'll give some examples -

2 = ?

Well, we see that 1 + 4 = 5, which means if we take 5 - (1 + 4), we get 0. This is good! Why? Well, we can then add 2 and be done. i.e.

2 = 5 - (1+4) + 2 (notice how I'm being careful with parentheses here - 5 - (1+4) is not the same as 5 - 1 + 4 because of PEMDAS!)

10 = ?

Well, it turns out that there may be several ways of solving this one. Since we haven't already, let's try using exponentiation (remember, an exponent refers to the number of times you need to multiply a number to itself. For example, 2⁴ = 2*2*2*2)

In this case, let's try to get rid of some of the options -

How about having 4^2? Well, that equals 16 (4*4). We also know that 5 + 1 = 6. This is good, because we can then write

10 = 4² - (5 + 1) (again, note the parentheses!)

For the rest of the numbers from 1-20, you do the exact same thing. Good luck and hope this helped!