We call a number sticky if every digit in the number is either a 3 or next to a 3 For example, the numbers 333, 3773 and 83 are all sticky, but the numbers 53225 and 3999 are not sticky.

How many positive 3-digit numbers are sticky?

Forumofweb2.0cal Feb 5, 2020

#1**+1 **

We can break into cases:

333 - 1 number

33* - 10 numbers

3*3 - 10 numbers

*33 - 10 numbers

*3* - 100 numbers

Total of 131 sticky numbers.

Guest Feb 5, 2020

#2**+1 **

I beleive that the other person over-counted.

Numbers of the form: *3* ---> 90 [don't count numbers starting with a '0']

Numbers of the form: 3*3 ---> 9 [actually, there are 10, but '333' has already been counted]

Numbers of the form: *33 and 33* have already been counted.

So, I think that there are only 99.

geno3141 Feb 5, 2020

#3**+1 **

a=1;b=0;c=0;p=0; cycle:d=a*100+b*10+c;if(b==3 or a==3 and c==3 or a==3 and b==3 or b==3 and c==3 , goto loop, goto next); loop:printd," ",;p=p+1; next:c++;if(c<10, goto cycle, 0);c=0;b++;if(b<10, goto cycle, 0);b=0;c=0;a++;if(a<10, goto cycle,0);print"Total = ",p

OUTPUT = 99 such numbers.

Guest Feb 5, 2020