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Split the Square (Posted on 2022-04-06)

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?

Submitted by Charlie

Rating: 5.0000 (1 votes)

Solution: (Hide)

The other 5-digit number is 88209:
88 + 209 = 297 = sqrt(88299)
bonus:
The split is shown on the line below the number and its square root:

136161 369 "1" "361" "6" "1" 136900 370 "1" "369" "00" 143641 379 "14" "364" "1" 171396 414 "17" "1" "396" 431649 657 "4" "3" "1" "649" 455625 675 "45" "5" "625" 494209 703 "494" "209" 571536 756 "5" "715" "36" 627264 792 "62" "726" "4" 826281 909 "826" "2" "81" 842724 918 "842" "72" "4" 893025 945 "8" "930" "2" "5" 929296 964 "929" "29" "6" 980100 990 "980" "10" "0" 982081 991 "982" "08" "1" 998001 999 "998" "001"
Where there's a leading zero, understand to separate it out as a stand-alone addend. Also there are alternative splits, for which you can see Larry's post.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Solution	tonny ken	2022-05-13 05:17:46
Longer Solutions	tomarken	2022-04-06 08:58:40
Solution	tomarken	2022-04-06 08:42:53
Solution	Larry	2022-04-06 08:24:12

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