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Comments (4)
aatifahmed
22 December 2008
The dog costs 4 dinar. The solution I am submitting below is encrypted so as not to take the fun out of your efforts! To decrypt use: www.rot-n.com The cipher used is ROT18-ROT5 & ROT13.
Note that Ali and Achmed had equal number of camels (lets call n). Hence; Total number of camels = 7n. Total money they receive for camels = 9n^2 The sheep could not be distributed evenly among them, hence its an odd number (lets say 7m+1). And lets say that cost of one goat is g and one dog is d. Therefore, 10*(7m+1)+g = 9n^2 Note g has to be even as the RHS is even. Also note that g is the unit digit of LHS, whereas the RHS is a square, leaving g to be only 6 or 4 (since 2 and 8 can never be unit digit of a square number, and 0 is not possible). Now, 7m + (10+g)/10 = n^2 Thus g has to divisible by 10, which leave g to be only 6. Since g is 6 and the distribution is equal so d has to be 4!!
alexonfyre
22 December 2008
I don't think it ever said they have equal number of camels aatifahmed...though it works if they do...I am pretty sure it is still true if they aren't equal numbers, however.
ChibiHoshi
18 March 2011
interestingly enough, if you look at a table of perfect squares, those with the tens place as an odd number (the only way there could be odd sheep) are always followed by a 6 (cost of a goat)
16,36,196,256,576,676,1156,1296,1936, etc.
So sheep-goat = dog
10-6 is 4
schizomidget
15 November 2016
The question is easy, all you need to do is set up some equations. But yeah, what interested me was that all perfect squares with an odd tens digit ended with a six. I wondered why so, and started coming up with explanations and this is what I've got:
0^2=00
1^2=01
2^2=04
3^2=09
4^2=16 ~ Ends with 6
5^2=25
6^2=16 ~ Ends with 6
7^2=49
8^2=64
9^2=81
I realized that it's not so much of a deal, it's just that all basic perfect squares that had an odd tens digit also ended with a 6. It just happens to be that way. So I guess this explains why this applies to all other numbers that are similar, since all of them (such as 196, 256, and 576) are squares of numbers that have a ones digit of 4 or 6.
Comments (4)
The dog costs 4 dinar.
The solution I am submitting below is encrypted so as not to take the fun out of your efforts! To decrypt use: www.rot-n.com
The cipher used is ROT18-ROT5 & ROT13.
Note that Ali and Achmed had equal number of camels (lets call n). Hence;
Total number of camels = 7n.
Total money they receive for camels = 9n^2
The sheep could not be distributed evenly among them, hence its an odd number (lets say 7m+1). And lets say that cost of one goat is g and one dog is d.
Therefore, 10*(7m+1)+g = 9n^2
Note g has to be even as the RHS is even. Also note that g is the unit digit of LHS, whereas the RHS is a square, leaving g to be only 6 or 4 (since 2 and 8 can never be unit digit of a square number, and 0 is not possible).
Now,
7m + (10+g)/10 = n^2
Thus g has to divisible by 10, which leave g to be only 6.
Since g is 6 and the distribution is equal so d has to be 4!!
I don't think it ever said they have equal number of camels aatifahmed...though it works if they do...I am pretty sure it is still true if they aren't equal numbers, however.
interestingly enough, if you look at a table of perfect squares, those with the tens place as an odd number (the only way there could be odd sheep) are always followed by a 6 (cost of a goat)
16,36,196,256,576,676,1156,1296,1936, etc.
So sheep-goat = dog
10-6 is 4
The question is easy, all you need to do is set up some equations. But yeah, what interested me was that all perfect squares with an odd tens digit ended with a six. I wondered why so, and started coming up with explanations and this is what I've got:
0^2=00
1^2=01
2^2=04
3^2=09
4^2=16 ~ Ends with 6
5^2=25
6^2=16 ~ Ends with 6
7^2=49
8^2=64
9^2=81
I realized that it's not so much of a deal, it's just that all basic perfect squares that had an odd tens digit also ended with a 6. It just happens to be that way. So I guess this explains why this applies to all other numbers that are similar, since all of them (such as 196, 256, and 576) are squares of numbers that have a ones digit of 4 or 6.
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