what will be the next number [ 32 , 57 , 201 , 210 , ? ]

Question

what will be the next number [ 32 , 57 , 201 , 210 ,  ?   ]

Answer 1

The trick to a questions like this, or ANY question that stumps you is to just do whatever you can think of and see where it takes you. Here's how I figured this out: I started by finding the difference between each pair of numbers, with the idea that I'd have to come up with a way to produce that difference so I could add it. (This might not have worked if the sequence involved multiplying, but you can't test everything at once.)

 

57 - 32 = 25

201 - 57 = 144

210 - 201 = 9

 

I noticed immediately that these differences are perfect squares (a number times itself). So then I tried to figure out how to come up with those numbers OR their square roots.

 

If you add the digits of the first number (32), you get 5. Square that and you get 25. Bingo!

     32 + 25 = 57.

Add the digits of 57, and the sum is 12. Square that and you get 144.

     57 + 144 = 201.

Add the digits of 201, and the sum is 3. Square that and you get 9.
      201 + 9 = 210.

 

So to find the next number:

Add the digits of 210, and the sum is 3 again. Square that and you get 9.
       210 + 9 = 219. This is the answer you asked for.

 

The number after that would be 2+1+9 = 12.   12 squared = 144.    219 + 144 = 363. Etc.