Among all 3-digit numbers in which no digit appears more than once, there is one special trait shared by...

arithmetic/digits/anomalous.cancellation New

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Problem

Among all 3-digit numbers in which no digit appears more than once,
there is one special trait shared by the numbers 195, 265, 498 and ONE
other 3-digit number.

(1) What is the trait?
(2) What is the 4th number which shares this trait?

-- Jeff G <answrman@idt.net>

Show solution

(1) They are three-digit numbers ABC such that AB/BC = A/C, i.e., you
can "cancel" the Bs.

(2) The remaining number is 164:  16/64 = 1/4.

-- Fred W. Helenius <fredh@ix.netcom.com>