perplexus.info :: Numbers : What is RUST?

What is RUST? (Posted on 2007-02-23)

Every day, Lucas receives a cube of metal whose side is between 9.5 and 10.5 meters. He melts the cube down and uses the resulting metal to make smaller cubes, whose sides are all between 9.5 and 10.5 centimeters, leaving no metal left over.

One day Lucas determined that he had made the smallest number of cubes he could under these conditions. It was a 6-digit number, call it abcdef, but not necessarily implying that there are no duplicate digits.

Lucas decided to make a cryptarithm using his number:

 RSTSTS
+RTRUTT
 abcdef

where each of the capital letters represents a distinct digit, the same digit for each occurrence of that letter.

What is RUST?

Submitted by Charlie

Rating: 4.5000 (2 votes)

Solution: (Hide)

Since the large cubes might be only 950 cm on a side and the small ones as large as 10.5 cm, the smallest number of cubes that Lucas could make would be ceil(950^3 / 10.5^3) = 740633. (The ceil function is the smallest integer greater than or equal to the argument. The floor function can't be used, as that would leave metal left over.)
Solving the cryptarithm, RUST is 3876.
From Enigma No. 1426 by Keith Austin, New Scientist, 20 January 2007

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2022-08-12 22:29:07
re(3): Solution	brianjn	2007-02-24 08:12:31
re(2): Solution	hoodat	2007-02-24 01:58:01
Iron Oxide	brianjn	2007-02-23 22:17:20
re: Solution	Art M	2007-02-23 18:38:33
Solution	hoodat	2007-02-23 15:47:48

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