數學思考題~(唔該...快!)

I am using the fastest term to show the answer, if there's something you don't know, see the explanation at the very below.

For 1, that's the easiest.
lcm(8,9)+2 is the answer
i.e. 72+2=74.

For 2, let the number be x.
20≡1(mod x)
50≡1(mod x)
so,
20+1=21≡0(mod x)
50+1=51≡0(mod x)
take gcd(21,51)
i.e. 3, the answer.

For 3, easy but difficult to explain.
........A............B
........╱￣￣￣￣╲
......╱....................╲
....╱........................╲ F
.C.╲........................╱
.......╲................... ╱
.........╲________╱
........D...............E
This is a hexagon. join AD, DF, AE.
You will find what you want.

For 4, easy!
You should see this if you see from the top:
⊕
ans you should see this if you see from the side:
曰
Ans is 8.
This is the three cut. Difficult to understand?
I explain in this way.
横切一下: 2 pieces
直切十字-兩下: 8 pieces.

That's all you want.

some terms i used:
lcm() The LCM of n numbers (n>2)
gcd() The HCF of n numbers (n>2)
x≡y(mod z) the remainder y while dividing x by z
hope you can learn more from here.

2008-01-19 17:01:17 補充：
sorry there's something wrong with 2it should be this:For 2, let the number be x.20≡1(mod x)50≡-1(mod x)so,20 1=21≡0(mod x)50 (-1)=49≡0(mod x)take gcd(21,49)i.e. 7 is the answer.

1.)某數除以8和9都欠2,某數最小是___72_________.
2.)20除以某數欠1,50除以某數餘1,某數最大是____99_______.
3.)在正六邊形的六角畫上三條直線
4.)若把長方體蛋糕切3刀,最多可將蛋糕分割為_6____小塊

我只知道第一條是70!

1)8 和 9 的 L.C.M 是 72
72 - 2 = 70
某數最小是70

2)20+1 = 21 = 7x3
50-1 = 49 = 7x7
某數最大是7

3)設正六邊形的6點是A,B,C,D,E,F

...A ____B
F ／........ ＼C
.. ＼____ ／
.... E......D

連接AC,CE,EA

4)最多可將蛋糕分割為8小塊

第四條:
可以最多有8件
先係十字割法, 變成4件，
再橫向切割一刀, 咁就有8件啦!!