Puzzle 15 : All but two

Solution to puzzle 14

Huh, sending more money would have been much easier than this puzzle.

     SEND
    MORE
  MONEY

We have to find values for S,E,N,D,M,O,R,Y (8 digits out of 10). 

Now, we're adding two 4-digits numbers. 

Since 9999+9999 < 20000, M cannot be >=2.
And by the "usual rules" for this kind of question, it can't be 0. So M=1.
Now, looking at the fourth (left-most) column, we have either S+1>=10 (if there's no carry) or 1+S+1>=10 (if there's carry). So S=8 or 9, and O=0 or 1. Since 1 is already taken, O=0 
In the third column, we can't have E+0=N (no carry), so E+1=N and there's carry from the second column. 
 So in the second column either N+R=10+E=9+N, and R=9, or there's carry and 1+N+R=10+E=9+N, and R=8. So R=8 or 9, just like S.
IF S=8 and R=9,we're looking at

  8END
+ 109E
======
 10NEY

But this cannot possibly work: we need to get either E+0=10+N or 1+E+0=10+N in the third column, to get carry in the fourth column. Neither is possible (we've already used up both 9 and 0). So...

S=9 and R=8.
We're looking at

  9END
+ 108E
======
 10NEY

We've already used up the digits 0,1,8,9, and N=E+1, so the only choices for E are 6,5,4,3,2.

We know we must have carry from the first column into the second, so D+E>=10. D is at most 7, so we immediately rule out E=2 (7+2<10). Also E=3 is impossible (because then either D=7 and Y=0=O, or D<7 and E+D<10, both of which are impossible).

If E=4, then D=7 or D=6 don't work (because then Y=1 or Y=0, and both are already taken), and D<6 doesn't work because then E+D<10.

If E=6 then N=7, so D<=5. But D=5 yields Y=1 and D=4 yields Y=0, both taken, and D<=3 gives E+D<10.

So E=5 and N=6. D=7 (the alternative, D<=4, is again too small), so Y=2 and the solution is

  9567
+ 1085
======
 10652

 I have borrowed this solution from https://everything2.com/title/send+more+money+solution 

Thank you everything.

Puzzle 15 : All but two

I have borrowed this puzzle from genius puzzles website.

I was invited to a pet show by a colleague. Since I was a bit busy that day, I sent my brother to the show. When he returned back I asked him about the show. He told me that all except two animals were fishes, all except two animals were cats and all except two entries were dogs.

Can you tell me how many animals of each kind were present in that pet show?  

Bonus

The question states that you have to form all the numbers from 1 to 100 using the digits of the year 2020 and the mathematical operators + - X / ! !! () and sqrt and ^. All the digits have to be used. I know few of you are jumping up from excitation. 

 e.g.

1 = 2/2 + 0+0

2 = 2 - 2 + 0!+ 0!

3 = 2^2 - 0! + 0

4 = 2+2+0+0

5 = 2+2+0!+0

and so on.

 This is the website and where you can send solution .