Brain Teasers Optical Illusions Puzzle Hunts Codes & Ciphers Mechanical Puzzles
Personal Links
Browse Teasers
Search Teasers

12-digit Oddities

Math brain teasers require computations to solve.

 

Puzzle ID:#43854
Fun:*** (2.46)
Difficulty:**** (3.22)
Category:Math
Submitted By:javaguru*us**

 

 

 



What characteristic do these three 12-digit numbers share with each other, but with no other 12-digit number?

100307124369
111824028801
433800063225

Open Calculator


Answer

They are all square numbers:

100307124369 = 316713^2
111824028801 = 334401^2
433800063225 = 656635^2

The sum of their digits are square numbers:

1+0+0+3+0+7+1+2+4+3+6+9 = 36 = 6^2
1+1+1+8+2+4+0+2+8+8+0+1 = 36 = 6^2
4+3+3+8+0+0+0+6+3+2+2+5 = 36 = 6^2

The sum of their digit pairs are square numbers:

10+03+07+12+43+69 = 144 = 12^2
11+18+24+02+88+01 = 144 = 12^2
43+38+00+06+32+25 = 144 = 12^2

The sum of their digit triplets are square numbers:

100+307+124+369 = 900 = 30^2
111+824+028+801 = 1764 = 42^2
433+800+063+225 = 1521 = 39^2

The sum of their digit quadruplets are square numbers:

1003+0712+4369 = 6084 = 78^2
1118+2402+8801 = 12321 = 111^2
4338+0006+3225 = 7569 = 87^2

The sum of their digit sextuplets are square numbers:

100307+124369 = 224676 = 474^2
111824+028801 = 140625 = 375^2
433800+063225 = 497025 = 705^2

Hide




What Next?

  
  

See another brain teaser just like this one...

Or, just get a random brain teaser

If you become a registered user you can vote on this brain teaser, keep track of
which ones you have seen, and even make your own.

 



Back to Top
   


Online Now
15 users and 676 guests

Users In Chat
autumn
Follow Braingle!
Fold 'N Fly Paper Airplanes
Easy to follow folding instructions and videos.
Copyright © 1999-2017 | FAQ | Widgets | Links | Green | Subscribe | Contact | Privacy | Conditions | Advertise | Braingle Time: 2:14 pm
Sign In Create a free account