Last night a puzzle was presented to me by my friend, a mathematician a.k.a. W.G. i.e. the Wise Guy.
He said: "I provide you a number S which is the sum of my secret
3 digit number X and 2 two-digit numbers derived from X by erasing one of its digits.
S is a 3 digit number composed of distinct digits.
I want you, using no computation aids, just your brains, pen and paper to solve my conundrum.
The sum is 439 - What is my original number?"
Needless to say it was solved in no time, you can treat it
as a d1 entry and handle it p&p.
But it inspired the following generalization addressing the perplexus society, rather d3:
There are plenty of 3 digit numbers using 3 distinct digits in the range of 102 to 987 (i. how many?).
Ii. How many, if used as S in the puzzle will provide a valid and unique X?
iii. How many yield: no solution?
iv. How many, if any, 2 or more answers?
I see that I have some different totals than Charlie, one example is S=125 for which I found secret number X=105. 105 + 05 + 15 = 125. In this case, I used 05 as one of the "2-digit numbers" and maybe a leading zero disqualifies it as a valid 2-digit number. I'm not sure if this accounts for all of the differences in our answers, but it seems like a good possibility.
How many S have unique X? 51
How many S have no solutions? 14
How many S have multiple values for X? 583
S values with unique Secret Numbers
{125: [105], 132: [106], 138: [109], 146: [122], 163: [135], 167: [137], 169: [138], 172: [144], 178: [147], 180: [148], 186: [160], 192: [163], 201: [172], 203: [173], 206: [146], 207: [175], 209: [176], 218: [185], 239: [163], 260: [220], 319: [271], 326: [252], 328: [280], 391: [327], 429: [357], 435: [350], 438: [366], 457: [359], 476: [372], 478: [416], 539: [452], 548: [461], 590: [520], 607: [479], 609: [483], 649: [538], 653: [551], 658: [547], 675: [605], 719: [583], 721: [627], 740: [640], 759: [633], 762: [649], 768: [642], 806: [672], 860: [743], 869: [719], 871: [747], 937: [779], 958: [836]}
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Posted by Larry
on 2023-05-23 12:21:16 |
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