Brain Teasers
A Five Digit Palindromic Square
There is a five digit square number that is palindromic, and each digit is also a nonzero square number.
What is it?
What is it?
Hint
Of course, it must be the square of a palindromic number. Therefore, when you multiply its square root by itself, there's no carrying, because carrying will break the palindrome. And therefore...Answer
44944=212^2.Hide Hint Show Hint Hide Answer Show Answer
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I'm sure there are others as well, but I prefer this one because it is the first (lowest): 10201 = 101^2.
Thanks! More number puzzles, please!
Thanks! More number puzzles, please!
Ooops - sorry! I just re-read your question, and realize I hadn't read it correctly the first time. I retract my previous comment!
Yes, I had
12321=111^2, until I re-read the question.
12321=111^2, until I re-read the question.
you know 1 is also a palindrome
Yeah, but 1 isn't 5 digits.
Nice teaser! I like how at first it seems like a brute-force approach, but that it surrenders nicely to simple analysis. I managed to find it on my third try!
I tried 122^2, 211^2 and then 212^2 based on the idea that the number squared would need to consist of only 1s and 2s so that it generated single-digit squares where each column of the product could sum without a carry. Also, since the middle column of the product sum would add three numbers together from the product, it would have to either be 1+1+2 = 4 or 4+4+1 = 9. That meant the number HAD to have at least one 2. There are only seven numbers (112, 121, 122, 211, 212, 221, 222) that meet the criteria, so I just started trying them.
I tried 122^2, 211^2 and then 212^2 based on the idea that the number squared would need to consist of only 1s and 2s so that it generated single-digit squares where each column of the product could sum without a carry. Also, since the middle column of the product sum would add three numbers together from the product, it would have to either be 1+1+2 = 4 or 4+4+1 = 9. That meant the number HAD to have at least one 2. There are only seven numbers (112, 121, 122, 211, 212, 221, 222) that meet the criteria, so I just started trying them.
I'm sorry but this tease has many flaws as even 121^2 would give 14641 which imo is also a 5 digit palindrom and a square
... but not one in which every digit is a perfect square. RTQ
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