多棒啊！
What a Trit!
题目详情
Terniquaternaria 国家采用了不寻常的数字系统。其 数字以 4 为基数表示，但只有三个“数字”： 0、1 和 T，其值为 (-1)。例如，号码“1T01” 对应于通常十进制中的数字 49（即 +14^3-14^2+04^1+14^0）。由于缺少第四位数字，许多 数字，例如 29，没有直接的表示形式。相反， Terniquaternaria（称为“Trits”）的居民将他们表示为 两个可表示数字的商（如果可能）。例如， 29 可以写成 (1100T/1TT) 或 (11111T/1T0T) 等 变体。
Decimus 刚刚登陆 Terniquaternaria，需要写下他的 录取表上的护照号码（524293）。是否可以？如果是这样的话， 怎么写呢？如果不是，你能证明不可能吗？
The country of Terniquaternaria follows an unusual numeral system. Its numbers are expressed as in base 4, but there are only three “digits”: 0, 1 and T, which has value (-1). For instance, the number “1T01” corresponds to the number 49 in the usual decimal system (i.e. +14^3-14^2+04^1+14^0). Due to the lack of a 4th digit, many numbers, such as 29, have no direct representation. Instead, the inhabitants of Terniquaternaria (called “Trits”) express them as the quotient of two representable numbers (when possible). For instance, 29 could be written as (1100T/1TT) or (11111T/1T0T), among other variants.
Decimus just landed in Terniquaternaria and needs to write down his passport number (524293) on the admission form. Is it possible? If so, how can it be written? If not, can you prove impossibility?
解析
这个月的谜题实际上是可以解决的，并且有多个正确的答案 解决方案。一个例子是 1TTTTTTTTT1TTTTTT00T0000011/111111111T0000001。这些技巧，当 转换为基数10，表示比率3002408341848069/5726584833 = 524293。事实证明，每个奇数整数都可以写成 可表示的数字，虽然证明远非微不足道，但这里是 一篇关于它的论文。
恭喜所有找到正确解决方案的人！
Original Explanation
This month’s puzzle was in fact solvable, and had multiple correct solutions. One example is 1TTTTTTTTT1TTTTTT00T0000011/111111111T0000001. These trits, when converted to base 10, represent the ratio 3002408341848069/5726584833 = 524293. It turns out every odd integer can be written as a ratio of representable numbers, although the proof is far from trivial, here is a paper about it.
Congratulations to everyone who found a correct solution!