## Puzzle #167: 4 Rats in a Star

Yet another wonderful puzzle from the NSA collection. Please do have your children try this one!

RATS x 4 = STAR

Each instance of a letter stands for the same digit, no two letters represent the same digit, and R cannot be 0. Which digits do the four letters represent?

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy fitting 4 rats into a star!

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### 3 Responses to Puzzle #167: 4 Rats in a Star

1. mashex says:

We can see that S times 4 should be R, hence R is 1 or 2, or else it would end in a 5 digit number. Also R should be 2 as no multiple of 4 ends with 1. And we can say that S is either 3 or 8 because those have the 2 multiples that end in 2. 3×4=12 and 8×4=32.And as we have a number times 4 ending in 2, the only possible number is 8. So now we know the number is 2AT8, A has to be less than 5, so with a little bit of trial and error, we will get 2178.

2. Prakhar says:

2178

3. Pratik Poddar says:

Solution:
RATS 8000 (Since ATS*4>2)
S>=8
So S=8

8000+AT*40+32=8000+10*TA+2
AT*4+3=TA and R=2, S=8
AT*4+3<100
AT*4<97
AT A is odd
A = 1

43+T*4=10*T+1
T=7

Check 2178*4=8712