12digit Oddities
Math brain teasers require computations to solve.
What characteristic do these three 12digit numbers share with each other, but with no other 12digit number?
100307124369
111824028801
433800063225
Hint316713
334401
656635
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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
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