FMM19 - Revision history

Admin at 21:42, 31 January 2020

2020-01-31T21:42:18Z

← Older revision		Revision as of 21:42, 31 January 2020
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	A telephone number belongs to <math>A \bigcap B</math> if and only if D1 = D4 = D5 = D2 = D6 = D3 = D7, so <math>n(A \bigcap B) = 10</math>.		A telephone number belongs to <math>A \bigcap B</math> if and only if D1 = D4 = D5 = D2 = D6 = D3 = D7, so <math>n(A \bigcap B) = 10</math>.

	Thus, by the Inclusion ~~Exclusoin Princile~~,		Thus, by the Inclusion Exclusion Principle,

	<math>		<math>

Admin at 06:03, 31 January 2020

2020-01-31T06:03:56Z

← Older revision		Revision as of 06:03, 31 January 2020
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	& = & 10^3 \times 1 \times 10 + 10^3 \times 10 \times 1 - 10 \\		& = & 10^3 \times 1 \times 10 + 10^3 \times 10 \times 1 - 10 \\
	& = & 19,990		& = & 19,990
			\end{align}
	</math>		</math>

	}}		}}

Admin at 06:03, 31 January 2020

2020-01-31T06:03:36Z

@@ Line 10: / Line 10: @@
 <math>
 \times 9990 + 10 = 19,990
 </math>
 }}

Admin: Created page with "{{FMM |title=Radical Sums |problem= Call a seven-digit phone number D1 D2 D3 - D4 D5 D6 D7 '''memorable''' if the prefix sequence D1 D2 D3 is exactly the same as either of the..."

2020-01-31T05:58:38Z

Created page with "{{FMM |title=Radical Sums |problem= Call a seven-digit phone number D1 D2 D3 - D4 D5 D6 D7 '''memorable''' if the prefix sequence D1 D2 D3 is exactly the same as either of the..."

New page

{{FMM
|title=Radical Sums
|problem=
Call a seven-digit phone number D1 D2 D3 - D4 D5 D6 D7 '''memorable''' if the prefix sequence D1 D2 D3 is exactly the same as either of the sequences D4 D5 D6 or D5 D6 D7 (possibly both). Assuming that each Di can be any of the ten decimal digits 0, 1, 2, ..., 9, find the number of different memorable telephone numbers.

|solution=

There are 10,000 ways to write the last four digits D4 D5 D6 D7. Among those are 10,000 - 10 = 9,990 for which not all the digits are the same. For each of these, there are exactly two ways to adjoin the three digits D1 D2 D3 to obtain a memorable number. There are ten memorable numbers for which the last four digits are the same, for a total of

<math>
2 \times 9990 + 10 = 19,990
</math>

}}