The Museum of HP Calculators

HP Forum Archive 19

 Martin Gardner dies at age 95Message #1 Posted by Don Shepherd on 24 May 2010, 5:36 a.m. His obituary. Another one of the great ones passes. He revealed the fascinating side of mathematics to generations of readers through his books, articles, and Scientific American columns. He will be missed. Who will take his place? The guy who writes the comic strip Foxtrot has a mathematical leaning, but I doubt that a worthy successor to Mr. Gardner is likely, unfortunately. In honor of his passing, I propose an easy challenge for a programmable calculator. Identify the only number(s) such that the sum of the digits times the product of the digits equals the original number. And, no, 95 is not one of them: (9+5) * (9*5) =/= 95.

 Re: Martin Gardner dies at age 95Message #2 Posted by Paul Dale on 24 May 2010, 7:38 a.m.,in response to message #1 by Don Shepherd 0 and 1 both satisfy the conditions and I didn't even need a program. Add the restriction that there be two or more digits in the number. - Pauli Edited: 24 May 2010, 7:48 a.m. after one or more responses were posted

 Re: Martin Gardner dies at age 95Message #3 Posted by Paul Dale on 24 May 2010, 7:48 a.m.,in response to message #2 by Paul Dale To avoid a gross answer, there should be an additional restriction of all the digits being different. - Pauli

 Re: Martin Gardner dies at age 95Message #4 Posted by Don Shepherd on 24 May 2010, 8:41 a.m.,in response to message #3 by Paul Dale Quote: To avoid a gross answer, there should be an additional restriction of all the digits being different. : ) If you prefer, but eliminating gross answers may reduce the pool of correct answers by 50%!

 Re: Martin Gardner dies at age 95Message #5 Posted by Martin Pinckney on 24 May 2010, 10:47 a.m.,in response to message #4 by Don Shepherd Doesn't this restriction actually remove ALL correct answers but 2? I can't write the program, but I do know the correct answers. Does that count? [:-) Edited: 24 May 2010, 10:57 a.m.

 Re: Martin Gardner dies at age 95Message #6 Posted by Don Shepherd on 24 May 2010, 9:05 a.m.,in response to message #2 by Paul Dale Quote: Add the restriction that there be two or more digits in the number. Agreed.

 Re: Martin Gardner dies at age 95Message #7 Posted by Don Shepherd on 24 May 2010, 8:59 a.m.,in response to message #1 by Don Shepherd Now, let me turn this into a REAL challenge. Implement this on the 17bii+ using the solver.

 Re: Martin Gardner dies at age 95Message #8 Posted by Martin Pinckney on 24 May 2010, 7:37 p.m.,in response to message #1 by Don Shepherd O.K., here's the numbers. Somebody write a program to find them. 1 digit: 0,1 2 digit: 22 [answer: 4] 3 digit: Any combination of 123, 321, etc. [answer: 6] 4 digit: Any combination of 4211 (must have two 1's) [answer: 8] 5 digit: Any combination of 52111 (must have three 1's) [answer: 10] 6 digit: Any combination of 621111 (must have four 1's) [answer: 12] And so on. Any other combinations work?

 Re: Martin Gardner dies at age 95Message #9 Posted by Don Shepherd on 24 May 2010, 9:22 p.m.,in response to message #8 by Martin Pinckney Martin, those numbers don't satisfy the criteria: sum of digits (n) * product of digits(n) = n. For example, sod(22) * pod(22) = 4 * 4 = 16, not 22. The only numbers that work are 0 and 1 and 135 and 144. I've tried testing numbers up to several million and found no others. Don

 Re: Martin Gardner dies at age 95Message #10 Posted by Martin Pinckney on 25 May 2010, 2:28 p.m.,in response to message #9 by Don Shepherd I guess I misunderstood the criteria. I understood sum of digits = product of digits.

 Re: Martin Gardner dies at age 95Message #11 Posted by Don Shepherd on 25 May 2010, 5:35 p.m.,in response to message #10 by Martin Pinckney Yes, I see. That's a different problem, of course. I guess no one wants to try to do this on a 17bii using the solver. I was hoping to point out a way of exiting a loop early in the solver, which the manual says you cannot do. But you can. : )

 Re: Martin Gardner dies at age 95Message #12 Posted by Martin Pinckney on 26 May 2010, 10:47 a.m.,in response to message #11 by Don Shepherd Well, I don't have a 17bii or +, but I do have a 17b and a 27s, so I would like to know the trick you mentioned. Probably others would also, although I get the impression the most members here are more interested in traditional keystroke programming than the Solver.

 Re: Martin Gardner dies at age 95Message #13 Posted by Don Shepherd on 26 May 2010, 1:07 p.m.,in response to message #12 by Martin Pinckney Martin, I wrote this little article 3 years ago for HCC2007. It describes the trick.

 Re: Martin Gardner dies at age 95Message #14 Posted by Antonio Maschio (Italy) on 26 May 2010, 4:38 a.m.,in response to message #1 by Don Shepherd Well, it's a very sad day. Martin Gardner was very popular even here in Italy. Ciao. -- Antonio

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