Question

how many 2 digit numbers have tens digit smaller than the the unit digit​

Answer 1

Answer:

Note that the tens digit gives the number of smaller one digits:

10 is such a number but not 11,12 and so on … it is 1 number

20 and 21 are such numbers, but not 22,23 and so on … there are 2 such numbers.

30 , 31 and 32 are such numbers, but not 33, 34 and so on … there are 3 such numbers.

I think you get the pattern.

So we have:

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

and even thought this could be still be done by hand there is a formula for

0+1+2+3+…+n=n×(n+1)2

Here for n=9 this yields 45 so this is your answer.

Answer 2

$12..13..14..15..16..17..18..19 \\ \\ 23..24..25..26..27..28..29 \\ \\ 34..35..36..37..38..39 \\ \\ 45..46..47..48..49 \\ \\ 56..57..58..59 \\ \\ 67..68..69 \\ \\ 78..79 \\ \\ 89$

◆ ▬▬▬▬▬▬ ❴✪❵ ▬▬▬▬▬▬ ◆◆ TOTAL. 36. NUMBERS WILL BE THERE

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