23) If you have trouble visualising this, try 'mapping' each column and row to the letters. For example, looking at the second picture, Column 5 > Column 4 > Column 3 > Column 2 > Column 1. Do the same thing with the rows. Looking at the first picture, row 1 > row 2 > row 3 > row 4. Hint: Sort by rows first. If there are multiple entries in the same row, sort those by columns.ALSO if you could have a look at:
Question 23 is there any logical way to go about doing that, I having trouble folding it up and unfolding it in my head :O (please don't say draw map out and start doing it!), also you may want to have a look at the last question, Question 30Code:http://docs.google.com/viewer?a=v&q=cache:VUkDh8z6kwQJ:www.chiuchang.org.tw/modules/mydownloads/visit.php%3Flid%3D286+we+say+a+number+is+ascending+if+its+digits+are+strictly+increasing.+For+exmaple,189+and+3468+are+ascending+while+142+and+466+are+not.+For+which+ascending+3-digit+number+n+%28between+100+and+999%29+is+6n+also+ascending%3F&hl=en&gl=au&pid=bl&srcid=ADGEEShEbG423mHPBDUpCzh7NCiRak0S4nF_qRQkltAkGjbrM7UVZBYr-5Qw8MazU4HLQCMYZEgsCkwkxH1_SxBmkVm73bXW7wtoLunzJiYYmsDUWjhrPeir8NbfHwwPMYpNNN6RbEeK&sig=AHIEtbR6FdfPv58Qtfh1pIemcOsvUPJKvg
That seems insane..
30) Let the total number of rabbits initially be n and the number deposited at each house is x.
After the first house, we have n-x rabbits. We cross the bridge to double the number we have. So we now have 2n - 2x rabbits
After the second house, we have (2n - 2x) - x rabbits. We cross the bridge to double the number we have. So we now have 2(2n - 3x) = 4n - 6x rabbits
After the third house, we have (4n - 6x) - x rabbits. We cross the bridge to double the number we have. So we now have 2(4n-7x) = 8n - 14x rabbits
After the fourth house, we have (8n - 14x) - x rabbits. We cross the bridge to double the number we have. So we now have 2(8n-15x) = 16n - 30x
At the fifth house, we have (16n-30x) - x rabbits, which equals 0 as we now have no more rabbits.
So 16n - 31x = 0. To find the minimum number of rabbits required, think about this logically:
the least amount of rabbits he can leave at each house is 1. So let x = 1. If x = 1, then 16n = 31. n = 31/16. But this is not a whole number, so x cannot equal 1.
Instead of checking every single integer up, we can look at why x = 1 doesn't work -> 31 is not divisible by 16. So if we look for the least common multiple of 16 and 31, we can solve for n easily.
LCM of 31,16 = 496. Therefore we need 31x = 16n = 496 => (x = 16, n = 31)
This can be extended to any number m houses. If you look at the pattern generated on each step, the equation for the amount of rabbits is:
Where m = number of houses; n = initial number of rabbits; x = rabbits deposited at each house.