The number 10000 can be split into 100 + 0 + 0 = 100, which is sqrt(10000).
That's rather banal, but there are two other such 5-digit numbers.
One is 55225:
5 + 5 + 225 = 235 = sqrt(55225)
What is the other one?
Each digit must be used exactly once, in proper order.
Bonus:
How many such 6-digit squares can you find?
For 5 digits, I found the solution 88209:
88 + 209 = 297 = sqrt(88209)
For 6-digits I found the following solutions:
sqrt(136161) = 369 = 1 + 361 + 6 + 1
sqrt(136900) = 370 = 1 + 369 + 0 + 0
sqrt(143641) = 379 = 14 + 364 + 1
sqrt(171396) = 414 = 17 + 1 + 396
sqrt(431649) = 657 = 4 + 3 + 1 + 649
sqrt(455625) = 675 = 45 + 5 + 625
sqrt(494209) = 703 = 494 + 209
sqrt(571536) = 756 = 5 + 715 + 36
sqrt(627264) = 792 = 62 + 726 + 4
sqrt(826281) = 909 = 826 + 2 + 81
sqrt(842724) = 918 = 842 + 72 + 4
sqrt(893025) = 945 = 8 + 930 + 2 + 5
sqrt(929296) = 964 = 929 + 29 + 6
sqrt(980100) = 990 = 980 + 10 + 0
sqrt(982081) = 991 = 982 + 0 + 8 + 1
sqrt(998001) = 999 = 998 + 0 + 0 + 1
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Posted by tomarken
on 2022-04-06 08:42:53 |
Solution
