Wednesday, March 25, 2009
Round 304
Sunday, March 22, 2009
Reviving the blog
However, we do not guarantee to post solutions at the time of the puzzle. Instead, we create an empty page and allow discussing through comments for each puzzle (Thanks to the advance posting feature from Blogger). We will post solutions when we have free time (mostly during weekend).
In this way, some people can't complain that they can't get into first 250 because of our site. However, we still provide solutions/hints for those who struggle. So I hope everyone will be happy.
LC Solver
Thursday, March 19, 2009
Round 303
Date Rewarded: March 26th, 2009. (estimated)
Rearrange the letters in the following phrase to come up with a Neopian word or phrase:
ROTATE SOON VIA RAIL
Submit only the answer with no other information, otherwise your answer will be marked as incorrect!
Steam Train Gummies
Click to show/hide hint
Thursday, March 12, 2009
Round 302
Date Rewarded: March 17th, 2009.
271 - 482 = 436
148 + 591 = 866
4881 + 8914 = 6562
8827 * 1178 = ?
Do NOT show your work; submit only a single number, with no punctuation, as your answer.
Rotawheel
Click to show/hide solution
To be easy to work on this problem, we convert all the digits into alphabetical letters in the following scheme: a = 1, b = 2, c = 3, d = 4, e = 5, f = 6, g = 7, h = 8, i = 9. Then we have three equations:
bga = dhb + dcf (1)
adh + eia = hff (2)
dhha + hiad = fefb (3)
Before we solve the problem, we have to assume that each letter represent a unique digit (distinct property.) For example, if a is 4, then b must not be 4. Also, all the digits in the hundreds' places in (1) and (2) and thousands' places in (3) must not be 0.
If we look at the equation (1) at the hundreds' place, we have b = d + d. So, we know that 1 <= d <= 4 because d can't be 0 and if d >= 5 then b is not a digit. There are four cases:
- d = 1: b can be either 2 or 3 (in the case of carry from the tens' place.)
- d = 2: b can be either 4 or 5.
- d = 3: b can be either 6 or 7.
- d = 4: b can be either 8 or 9.
If we look at the equation (3) at the unit's place, we have a + d = b. Then, the four cases will be following:
- d = 1:
b = 2 => a = 1(violate the distinct property), b = 3 => a = 2 - d = 2:
b = 4 => a = 2(violate the distinct property), b = 5 => a = 3 - d = 3:
b = 6 => a = 3(violate the distinct property), b = 7 => a = 4 - d = 4:
b = 8 => a = 4(violate the distinct property), b = 9 => a = 5
If we look at the equation (1) at the unit's place, we have a = b + f. Then, the four cases will be following:
- d = 1: a = 2, b = 3 => f = 9
- d = 2: a = 3, b = 5 => f = 8
d = 3: a = 4, b = 7 => f = 7(violate the distinct property)- d = 4: a = 5, b = 9 => f = 6
There are only three cases left after the last analysis. If we look at the equation (2) at the unit's place, we have h + a = f. Then, the three cases will be following:
- d = 1: b = 3, f = 9, a = 2 => h = 7
d = 2: b = 5, f = 8, a = 3 => h = 5(violate the distinct property)- d = 4: b = 9, f = 6, a = 5 => h = 1
There are only two cases left now. However, if we look at the equation (2) at the hundreds' place, we have a + e = h. In the last case, a = 5 and h = 1. It is impossible to get since h > a. Therefore, only the first case is correct. Then, we have: a = 2, b = 3, d = 1, f = 9, h = 7
Now, we look at the equation (2) at the tens' place. Since there is no carry on the unit's place addition, we can write: d + i = f <=> i = f - d = 9 - 1 = 8 (no carry either). Then, we look at the same equation at the hundreds' place, we can write: a + e = h <=> e = h - a = 7 - 2 = 5.
Then, we look at the equation (1) at the tens' place. Since there is a carry on the unit's place (a = 2 = 3 + 9 = b + f), we can write: g = h + c + 1 <=> g = c + 8. Since 1, 2, 3, 5, 7, 8, 9 are already taken. c and g can only be 0, 4 or 6. Only the pair c = 6 and g = 4 are satisfied this equation. Therefore, we have: a = 2, b = 3, c = 6, d = 1, e = 5, f = 9, g = 4, h = 7, i = 8.
Wednesday, March 4, 2009
Round 301
Wednesday, December 31, 2008
Round 292
Wednesday, December 17, 2008
Round 291
http://www.neopets.com/faerieland/hiddentower938.phtml
Use the second letter of each item to get the question and check the Hidden Tower for the answer. Good luck!