Write 1 to 10 using 3 and 5, each at least once, and using addition and subtraction. (For example, 7 = 5 + 5 – 3.)

We need to write numbers 1 to 10, using 3 and 5 only, irrespective of how many times we use 3 and 5, using addition and subtraction.

Take number 1,

We know (3 + 3) = 6, and (6 – 5) = 1

⇒ 1 = 3 + 3 – 5

Take number 2,

Simply subtract 5 and 3.

⇒ 2 = 5 – 3

Take number 3,

We know, (8 – 5) = 3.

And 8 can be written as (5 + 3), then subtract 5 from the addition.

We get, 3 = (5 + 3) – 5

⇒ 3 = 8 – 5

Take number 4,

We know, (9 – 5) = 4.

And 9 can be written as (3 + 3 + 3), then subtract 5 from the addition.

We get, (3 + 3 + 3) – 5 = 9 – 5 = 4

⇒ 4 = 3 + 3 + 3 – 5

Take number 5,

Just cancel 3 from 3, then add 5 to it.

⇒ 5 = (3 – 3) + 5

Take number 6,

We know, (3 + 3) = 6 but we need to include 5 also. So, just add (5 – 5) to it, it would not mean anything and won’t disturb the equation, while satisfy the question.

⇒ 6 = 3 + 3 + 5 – 5

Take number 7,

We know, (10 – 3) = 7.

And 10 can be written as (5 + 5), then subtract 3 from it.

We get, (5 + 5) – 3 = 10 – 3 = 7

⇒ 7 = 5 + 5 – 3

Take number 8,

We know, (5 + 3) = 8

⇒ 8 = 5 + 3

Take number 9,

Although 9 can be represented by several ways using 5 and 3.

One of the easiest way is:

We know, (3 + 3 + 3) = 9, then add (5 – 5) to it.

⇒ 9 = 3 + 3 + 3 + 5 – 5

Also, we know 9 = 15 – 6

Where 15 = 5 + 5 + 5

And 6 = 3 + 3

So, 9 = (5 + 5 + 5) – (3 + 3)

⇒ 9 = 5 + 5 + 5 – 3 – 3

Take number 10,

We know, (5 + 5) = 10.

Just add (3 – 3) to it, it won’t affect the equation.

⇒ 10 = 5 + 5 + 3 – 3

Hence, we have found the answers.