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Full Version: Martin Gardner dies at age 95
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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.

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

To avoid a gross answer, there should be an additional restriction of all the digits being different.

- Pauli

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%!

Now, let me turn this into a REAL challenge. Implement this on the 17bii+ using the solver.

Quote:
Add the restriction that there be two or more digits in the number.

Agreed.

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.

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?

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

I guess I misunderstood the criteria. I understood sum of digits = product of digits.

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.

: )

Well, it's a very sad day. Martin Gardner was very popular even here in Italy.

Ciao.

-- Antonio

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.

Martin, I wrote this little article 3 years ago for HCC2007. It describes the trick.