今天我们给出第六组袋鼠竞赛的题目（每个年级组一道题），并给出第五组题目（见《袋鼠数学竞赛题选（五）》）的解答。

1-2年级组

In Baby Roo's house, each room is connected to any neighboring room by a door as shown in the picture. Baby Roo wants to get from the room A to the room B. What is the least number of doors that he will need to go through?

在Baby Roo的房子里，每个房间和与它相邻的房间之间都有一扇门相连，如下图。Baby Roo想从房间A走到房间B。他最少需要经过多少扇门？

3-4年级组

Three ropes are laid down on the floor as shown. You can make one big, complete loop with three other pieces of rope. Which of the ropes shown will give you one big loop?

三条绳子如下图那样放置在地板上。你可以利用另外三条绳子，与这三条绳子一起构成一个大的绳圈。你可以用下面哪组绳子做到？

5-6年级组

A train has 12 coaches. Each coach has the same number of compartments. Mike is travelling in the third coach and in the 18th compartment from the engine. Jane sat in the 7th coach in the 50th compartment from the engine. How many compartments are there in each coach?

一列火车有12节车厢，每节车厢里有相同数量的隔间。Mike位于第三节车厢，坐在从火车头数过来的第18个隔间。Jane位于第七节车厢，坐在从火车头数过来的第50个隔间。每节车厢里有多少个隔间？

7-8年级组

Two pieces of rope have lengths 1 m and 2 m. Alex cuts the pieces into several parts. All the parts have equal lengths. Which of the following could not be the total number of parts he obtains?

两条绳子的长度分别为1米和2米。Alex把它们剪成小段，每段绳子都一样长。下面哪个数不可能是他得到的绳子的段数？

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下面是第五组题目的参考答案和解析。

1-2年级组

Agatha, the hen, lays white and brown eggs. Lisa puts six eggs in the box below. Two brown eggs cannot touch each other. At most, how many brown eggs can Lisa put in the box?

母鸡Agatha会下白色和褐色的蛋。Lisa把6个蛋放在下图所示的盒子里，使得任何两个褐色的蛋都不相互接触。Lisa最多可以在盒子里放多少个褐色的蛋？

3-4年级组

In the figure, we see an island with a highly indented coastline and several frogs. How many of these frogs are sitting on the island?

下图中有一个海岸线非常弯曲的岛，还有几只青蛙。这些青蛙中有多少只在岛上？

【答案：B】首先确定，椰子树应该长在岛上。以此为起点，沿着海岸线可以确定哪些青蛙的位置在岛上。见下图，用紫色标注的青蛙都在岛上。

5-6年级组

In a 4-digit number ABCD, the digits A, B, C and D are in increasing order from left to right. What is the largest possible difference BD-AC of the 2-digit numbers BD and AC?

在一个四位数ABCD中，从左到右的数字A，B，C，D越来越大。用这些数字组成两个两位数BD和AC。它们的差BD-AC最大可以是多少？

由于C和D都比B大，所以B最大只能是7。A最小是1，所以B-A的值最大是6。此时必须有C=8，D=9。

7-8年级组

Rachel added the lengths of three sides of a rectangle and got 44 cm. Heather added the lengths of three sides of the same rectangle and got 40 cm. What is the perimeter of the rectangle?

有一个长方形。Rachel随意选取了它的其中三条边，把它们的长度相加，得到的和为44厘米。Heather也选了它的三条边并将它们的长度相加，得到的和为40厘米。这个长方形的周长是多少？

【答案：B】长方形的四条边分别是两条长边和两条短边。Rachel和Heather分别去掉了一条边。因为Rachel得到的和比Heather大，所以Rachel去掉的是短边，Heather去掉的是长边。即，Rachel选择了两长一短，Heather选择了两短一长。

44+40=84，这是三条长边和三条短边的长度之和。84÷3=28，这是一条长边和一条短边的长度之和。长方形的周长是它的两倍。