World!OfNumbers |
WON plate 167 | |
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[ The first edition of this book appeared in February, 2004 by the publisher Sura Books (Pvt) Ltd., Chennai, India [ article by yours truly PDG ] The smallest factor from the output list happens with You will surely like this nice pandigital with a _unique_ solution
The largest 5-digit factor is also the right substring of the pandigital itself ! Two factors occur each four times nl. 69135 and 98640 !
Nine pandigitals can be factorized into twin sets of 5-digitfactors of which three are included in episode 33 (pp. 20). The remaining six twin sets are
1239756840 = 18495 * 67032
1479635280 = 15864 * 93270
1954283760 = 37620 * 51948
2483619750 = 26475 * 93810
4031985672 = 49137 * 82056
4293156780 = 49260 * 87153 I did a likewise investigation but with ninedigitals this timeexpressed as a product of a 4-digit and a 5-digit factor. The computer rendered 346 solutions ! The smallest such ninedigital is The smallest 4-digit factor happens with We notice that 5-digit number 98754 is the largest factor Here also two factors occur each four times
Now the reader is invited to multiply together 6351 * 9864 = 6264_6264 An eyecatching Parallel to episode 33 I compiled four ninedigital numbers
147963528 = 7932 * 18654
195428376 = 3762 * 51948
248361975 = 3975 * 62481
429315678 = 4926 * 87153 Note that the first one is very beautiful since the 4-digit 7932 * 18654 digit 0 ( # 16 ) digit 1 ( # 11 ) digit 2 ( # 24 ) digit 3 ( # 17 ) digit 4 ( # 21 ) digit 5 ( # 10 ) digit 6 ( # 7 ) digit 7 ( # 2 ) digit 8 ( # 5 ) digit 9 ( # 0 ) A _twofold_ solution pops up if we keep the seven identical
56738 * 92041 Two 10-digits contain more than seven identical digits
Restricting the remaining digits to be identical leads us
The third solution again reveals to us the presence of The extended versions of the Beast are available as well !
To conclude this expansion on the subject two equations
The palindrome 62226 will come back in another format, ** Inspired by B.S. Rangaswamy's book I set out to look for ninedigital numbers that are the product of two 5-digit factors and that taken together form pandigitals. 141 solutions came up which is a palindromic total ! The smallest one is 315867942 = 15486 * 20397 The largest one is 987561234 = 28179 * 35046 The uniqueness of the following result is that
The Beast took refuge in one of the 141 solutions !
** Episode 55 : Six Soldiers (p. 77) This chapter prompts you explore 10 digit numbers having six identical numerals positioned in a continuous line. While recomputing all the possible solutions (total of 44), including those with two 5-digit factors not evenlydivisible by 3, I stumbled over the following curios ¬ Particularly beautiful is this item because it Some not continuous solutions with only two distinct digits Also special is this item because the digits of the The first construct is with multiplicand 27489 and his
A second construct produces a ninedigital and a pandigital with
Finally three _still interesting_ leftovers from my search.
** Palindromes as products of two 5-digit factors. There are only ten palindromes consisting of nine digits
One anagrammatical combination shows up here.
Palindromes as products of a 4-digit and a 5-digit factor. There are three palindromes consisting of eight digits and
Five
One
Mixed anagram equations starting from a common factor. The first and the last two constructions are remarkable in the Many examples I found are displayed as well but without
Palindromic lookalikes. Behold the next two palindromes and get enchanted.
Compare the next two palindromes and get enchanted. The first equation is an 8-digit palindrome expressed as a product of a 4- and a 5-digit factor which taken together form a ninedigital. The second equation is a 9-digit palindrome identical to the previous one except for the extra middle digit 9 expressed as a product of two 5-digit factors which taken together form a pandigital.
There exist imho no better constructions that can synthesize this wonplate in such a beautiful way ! ** Scintillating equations with two 5-digit factors and their reversals.
Below is shown an exceptionally nice pair of equations.
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A000167 Prime Curios! Prime Puzzle Wikipedia 167 Le nombre 167 |

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