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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

429.0. "Only one digit known problem" by MENTOR::KOSTAS () Wed Jan 15 1986 09:46

This problem is to reconstitute the division:

             xxx) xxxxxxxx ( xx8xx
                  xxxx
                  ----
                    xxxx
                     xxx
                    ----
                      xxxx
                      xxxx
                      ----

where every  x  represents some digit, initial zero excluded.
This problem may seem more difficult that the "SEND MORE MONEY" problem,
since we do not know what digits are alike and which are different.
I know of one solution I woulder if there are more than one solution
to this.

Enjoy,

Kostas G.
<><><><><>

T.R	Title	User	Personal Name	Date	Lines
429.1		R2ME2::GILBERT		`Fri Jan 17 1986 12:44`	25
	The quotient is clearly 90809. We see that the 3-digit divisor xxx must satisfy: xxx >= 100 xxx * 8 < 1000 xxx * 9 >= 1000 so, 111 < xxx < 125. We can easily test each of these divisors, checking that it satisfies: 10 <= [90809xxx/10000] - 9xxx <= 99 10 <= [90809xxx/100] - 908xxx <= 99 The only value of the divisor in the range that satisfies this is 124. So, the solution is: 124 ) 11260316 ( 90809 1116 ---- 1003 992 ---- 1116 1116 ----
429.2	Another aproach to the solution of .0	THEBUS::KOSTAS	Kostas G. Gavrielidis <o.o>	`Sat May 31 1986 18:42`	48
	Where two digits are brought down at one step, it is clear that a zero occurs in the quotient. So it is x080x. Let us call the divisor D. Since 8D has but three digits, the other two multiples of D which contain four digits, must be each 9D, so the quotient is 90809. A tree digit number is less than 1000. Hense 8D < 1000 and so D < 125. A six digit number is greater than 99999 and when 9D is subtracted from the dividend, a six digit number remains, and the division comes out without remainder. Hense 809D > 99999 and so 492 d > 123 --- 809. It follows that D = 124. We have the product 124 * 90809 = 11260316 so we reconstitute the division as follows: 124 ) 11260316 ( 90809 1116 ---- 1003 992 ---- 1116 1116 ---- Enjoy, Kostas G.