有一百匹马,一百块瓦,马有三种,大马一马拉三块瓦、中马一马拉两块瓦、小马三马拉一块瓦,问大、中、小马各多少匹?

设大马有X匹,中马有Y匹,小马有Z匹.
X+y+z=100①
3x+2y+z/3=100②
由②得
9x+6y+z=300③
③-①得
8x+5y=200④
Y=(200-8x)/5
(x小于100,y大于0,x大于0,x,y都是整数）
根据为些条件,可以知
要想让Y大于0的整数,那么200-8x就一定要是5的倍数
用式子表示
200/5-(8/5)x=y
40-(8/5)x=y
从里这以在道x必为5的倍数,这符条件的数代入方程,得
X1=0 y1= 40 z1=60
X2=5 y2=32 z2=63
X3=10 y3=24 z3=66
X4=15 y4=16 z4=69
X5=20 y5=8 z5=72
X6=25 y6=0 z6=75

问题翻译：
1.
Satin dress Jiuqu pearl, is a soft satin across the Pearl (say the Chinese jade) zigzag holes.
2.
The mother child relationship identified one hundred mare and one hundred foal.
3.
Provisions of 100 proposal messengers days after the one hundred altar wine, eating one hundred sheep, but the sheep kneaded.
4.
Tang emperor to the ministers of pine one hundred, let Garl Donzanusson tell the roots and shoots.
5.
The night of entering the palace lost (also said to be identified the Wanxiang door inside the door).
6.
Identify the princes.
第一试：比赛开始,由于吐蕃以外的使臣们有势力,所以他们抢先取去,绞尽脑汁,怎奈几挽也没有穿过去.而聪慧的禄东赞坐在一棵大树下想主意,偶苫发现一只大蚂蚁,于是他灵机一动,找来一根丝线,将丝线的一头系在蚂蚁的腰上,另踊头则缝在绫缎上.在九曲孔眼的端头抹上蜂蜜,把蚂蚁放在另一边,蚂蚁闻到蜂蜜的香味,再借助禄东赞吹气的力量,便带着丝线,顺着弯曲的小孔,缓缓地从另一边爬了出来,绫缎也就随着丝线从九曲明珠中穿过.
翻译：The start of the game, because the outside of the envoys have power, so they have to take, but a few arm rack sth., also did not wear the past. The intelligent and Lu Dongzan sat under a big tree to idea, I felt that a big ant, he suddenly have a brain wave, found a piece of thread, a head of thread in the ant's waist, another head is sewn on the satin. Honey in the end nine hole cast, the ants on the other side, the ants smell the aroma of honey, then Lu Dongzan blowing force, and with a silk thread, along the curved holes, slowly crawled out from the other side, satin also along with the silk from the Jiuqu Pearl through.
第二试：比赛开始,但见各位婚使轮流辨认,有的按毛色区分,有的照老幼搭配,有提则以高矮相比,然而都弄错了.最后轮到禄东赞了,得到马夫的指教,他把所有的母马和马驹分开关着,一天之中,只给马驹投料,不给水喝.次日,当众马驹被放回马群之中,它们口喝难忍,很快均找到了各自的母亲吃奶,由此便轻而易举地辨认出它们的母子关系.紧接着,唐太宗李世宗又出题让指认百只雏鸡与百只母鸡的母子关系.这件事又把其他婚使难住了,谁也指认不清.禄东赞便把鸡珊赶到广场上,撒了很多食料,母鸡一见吃食,就“咯、咯、咯”地呼唤小鸡来吃,只见大多数小鸡跑到自己妈妈的颈下啄食去了.但是仍有一些顽皮的小鸡不听呼唤,各自东奔西跑地去抢食,于是禄东赞学起鹞鹰“瞿就儿——瞿就儿——”的叫声,鸡娃听见,信以为真,急忙钻到了各自母亲的翅膀下藏起来,母鸡与雏鸡的关系再被确认开来.
翻译：The start of the game, but see you married rotate identification, some of the hair color to distinguish, some as young and old is tie-in, mentioned in height compared, however, are wrong. Finally, when Lu Dongzan, get the advice, he put all the mares and foals separated off, one day, only to the pony feeding, no water to drink. The next day, when the foal is back on the horses, they thirst unbearable, soon found their mother milk, this will be an easy job to identify their mother child relationship. Then, Tang Taizong and Li Shizong set let mother child relationship identified 100 chickens and hens. This thing and the other marriage that stumped, who also said not clear. Lu Dongzan Bianba chicken Shan arrived on the square, and a lot of food, the hen saw feeding, "Luo, Luo, Luo" call a chicken to eat, but most chicks ran to her mother to the neck under the pecking order. But there are still some naughty chicken to call, each run around here and there to eat, so Lu Dongzan to learn the kite "Qu is son -- Qu is son --" the cry, chick heard, for gospel truth, quickly drill to hide their mother hen and chicken wings, the relationship between re confirmed.
第三试：比赛开始,别的使者和随从匆匆忙忙地把羊宰了,弃得满地又是毛,又是血；接着大碗地喝酒,大口地吃肉,肉还没有吃完,人已酩酊大醉,哪里还顾得上揉皮子.禄东赞则让跟从的一百名骑士排成队杀了羊,并顺序地一面小口小口地咂酒,小块小块地吃肉,一面揉皮子,边吃边喝边干边消化,不到一天的功夫,吐蕃的使臣们就把酒喝完了,肉吃净了,皮子也搓揉好了.
翻译：The start of the game, Messenger and his entourage hurriedly slaughtered, abandon all over the floor and hair, and blood; then the bowl to drink, mouth to eat meat, the meat is not finished, people have be completely drunken, where still attend to rubbing on the skin. Paul one hundred Knights East praise let and lined up to kill the sheep, and sequentially a sip sip wine, small pieces of meat, a rubbing the skin, eat and drink by doing digestion, less than a day, the Tibetan envoys had finished his drink, eat meat net, the son also rub the skin.
第四试：噶尔遂令人将木头全部运到河边,投入水中.木头根部略重沉入水中,而树梢那边较轻却浮在水面,木头根梢显而易见.
翻译：This was a wood are transported to the river, into the water. Wood root slightly heavier sink into the water, and the trees there is light but floating on the surface of the water, wood root tip obviously.
第五试：禄东赞想到初来乍到长安,路途不熟,为不致迷路,就在关键路段做了“田”字记号(也有说是涂上颜色).到了皇宫以后,皇帝又叫他们立即回去,看谁不走错路回到自己的住处.结果,禄东赞凭着自己事先做好的记号,再次地取得了胜利.
翻译：Lu Dongzan think new in Changan, journey is not ripe, is not lost, do the "Tian" word mark in key sections (there are said to be color). Subsequent to the palace, the emperor and let them go back immediately, see who is not going to return to their homes. The results, Lu Dongzan yourself well in advance of the mark, again to victory.
第六试：但见衣著华丽、相貌仿佛的300名(也有说500名或2500名)宫女,分左右两队依次从宫中排开,宛如300天仙从空中飘来,轻盈、潇洒、俊美,看的人眼花缭乱.其他使者都没有主意,不知哪位才是文成公主,惟独禄东赞因为事先得到了曾经服侍过公主的汉族老大娘的指教,知道了她的容貌身体特征：体态娟丽窈窕,肤色白皙,双眸炯炯有神,性格坚毅而温柔,右颊有骰子点纹,左颊有一莲花纹,额间有黄丹圆圈,牙齿洁白细密,口生青莲馨味,颈部有一个痣.禄东赞反复辨认,最后终于在左边排行中的第6位认出了公主.
翻译：But see the gaily dressed, looks like 300 (or 500 or 2500) the maid, two teams from the palace about turn up, like the 300 fairy wafted through the air, light, cool, handsome, see people see things in a blur. Other messengers have no idea, I do not know who is the Princess Wencheng, but Lu Dongzan because received advance once served the princess Han old woman's advice, know her face physical characteristics: body Juan Li slim, fair complexion, eyes one's eyes brimming with radiating vigour, character is fortitude and gentle, right cheek dice puncta, left cheek a lotus flower, forehead with Dan circle, teeth fine, sweet taste in Qinglian, neck has a nevus. Lu Dongzan repeated identification, finally in the ranking of sixth recognized the princess.

大马=X
中马=Y
小马=Z
X+Y+Z=100
3X+2Y+1/2Z=100
6X+4Y+Z= 200
(X+Y+Z=3X+2Y+1/2Z) X2
2X+2Y+2Z=6X+4Y+Z
Z=4X+2Y
X+Y+(4X+2Y)=100
5X+3Y=100
Y = (100-5X)/3
当 X = 16,y = 6.67
当 X = 12,y = 13.33
当 X = 8,y = 20
当 X = 4,y = 26.67
当 X = 0,y = 33.33
但马匹一定是整数.
如果全部100匹,大马是8,中马是20,那余下来的小马就是72了.
再来8匹大马共拖24块,20匹中马共拖40块,那72匹小马共拖36块,刚好是100砖