有没有这样一个完全平方数,各个数位上数字之和等于100?

题目

有没有这样一个完全平方数,各个数位上数字之和等于100?

答案

应该有,不过很难找,还不止一个.
如果这个题目改成：“有没有这样一个完全平方数,各个数位上数字之平方和等于100?”会容易点,也不少,但数都不小：
394^2=155236 (1 5 5 2 3 6 ) -->100 [found]
489^2=239121 (2 3 9 1 2 1 ) -->100 [found]
498^2=248004 (2 4 8 0 0 4 ) -->100 [found]
596^2=355216 (3 5 5 2 1 6 ) -->100 [found]
1492^2=2226064 (2 2 2 6 0 6 4 ) -->100 [found]
1748^2=3055504 (3 0 5 5 5 0 4 ) -->100 [found]
1775^2=3150625 (3 1 5 0 6 2 5 ) -->100 [found]
2248^2=5053504 (5 0 5 3 5 0 4 ) -->100 [found]
2259^2=5103081 (5 1 0 3 0 8 1 ) -->100 [found]
3166^2=10023556 (1 0 0 2 3 5 5 6 ) -->100 [found]
3571^2=12752041 (1 2 7 5 2 0 4 1 ) -->100 [found]
3940^2=15523600 (1 5 5 2 3 6 0 0 ) -->100 [found]
4797^2=23011209 (2 3 0 1 1 2 0 9 ) -->100 [found]
4890^2=23912100 (2 3 9 1 2 1 0 0 ) -->100 [found]
4980^2=24800400 (2 4 8 0 0 4 0 0 ) -->100 [found]
5506^2=30316036 (3 0 3 1 6 0 3 6 ) -->100 [found]
5960^2=35521600 (3 5 5 2 1 6 0 0 ) -->100 [found]
6261^2=39200121 (3 9 2 0 0 1 2 1 ) -->100 [found]
7499^2=56235001 (5 6 2 3 5 0 0 1 ) -->100 [found]