12-digit OdditiesMath brain teasers require computations to solve.What characteristic do these three 12-digit numbers share with each other, but with no other 12-digit number?
100307124369 111824028801 433800063225 
AnswerThey 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?
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