4 Digits and a Square
Target: 4 digit number
Criteria:
1. add the number formed by the first 2 digits to the number formed by the second 2 digits
2. the square of the results of step 1 equals the original 4 digit number
3. there is another number, with a 1000 difference, from the original number, which also complies with criteria in steps 1. and 2.
Criteria:
1. add the number formed by the first 2 digits to the number formed by the second 2 digits
2. the square of the results of step 1 equals the original 4 digit number
3. there is another number, with a 1000 difference, from the original number, which also complies with criteria in steps 1. and 2.
posted by Zaux at
9:04 AM
9 Comments:
9801
Nice one Pequod.
I don't think 9801 is valid with condition 3.
9801-1000=8801
88+01=89 and 89^2 !=7921
2025 works though
20+25=45
45^2=2025
AND
2025+1000=3025
30+25=55
55^2=3025
Cam
This post has been removed by a blog administrator.
That's it Cam ...
Was I too quick to praise? I didn't notice condition 3 when I complimented Pequod.
i thought it would be harder than i thought.
4 digits and a square
*1) 100x+y=(x+y)^2
100x+y+1000=100*(x+10)+y
*2) 100*(x+10)+y=((x+10)+y)^2
From *1
*1A) 100x+y=x^2+2xy+y^2
From *2
100x+y+1000=x^2+10x+xy+10x+100+10y+xy+10y+y^2
*2A) 100x+y+1000=x^2+2xy+y^2+10(2x+2y+10)
From *2A-*1A
1000=10(2x+2y+10)
1000=20x+20y+100
20x+20y=900
x+y=45
x=45-y
sub into *1
100x+y=(x+y)^2
100*(45-y)+y=(45-y+y)^2
4500-100y+y=45^2
-99y=45^2-4500
y=(45^2-4500)/(-99)
y=25
x=45-y=45-25=20
x=20
y=25
Answer:
The number is 2025.
The other number is 1000+2025=3025
Cam
Very nice Cam. Thanks for that.
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