Question

How many different 2-digit numbers are there with the following property: the tenth digit is greater than the units digit?

Answer 1

Explanation:

2 digit numbers are beetween 10 and 99

We are looking for numbers in wich the unit digits is less than the ten digit

we can make notice something about this numbers

• 10
• 20
• 30
• 40
• 50
• 60
• 70
• 80
• 90

0 is the smallest postive integer so all these numbers satisfy the condition

so we have now 9 numbers

here is another remark :

• 0 < 1 < 2 < 3 <4 <5 <6 < 7 < 8 < 9

numbers from 91 to 99 satisfy the condition except 99

so here are 8 other numbers

numbers from 80 to 89 satisfy the condition except 88 and 89

so here are 7 other numbers

the numbers that satisfy the keeps decreasing by 1 each time

• 8 (91⇒98)
• 7 81⇒88 + 80
• 6 71⇒76 + 70

• 5 61⇒ 65 +60
• 4 51⇒ 54 + 50
• 3 41⇒ 43 + 40
• 2 31⇒32 + 30
• 1 21 + 20

so the total number of numbers that satisfy the condition

9+8+7+6+5+4+3+2+1= 45