8×2= 16,

8×8=64;

(2)8+2= 10,

12+3= 15,

16+4=20,

So this digital tower can be completed as shown in the following figure:

2

2 2

2 4 2

2 8 8 2

2 16 64 ( 16) 2

1

2 4

3 6 9

4 8 12 16

5 ( 10) ( 15) (20) 25

Sixth grade Olympic math problem: looking for the law

There is often a cycle in finding regular questions, and the key to such problems is to find out the repeated content "groups" Then see how many such groups always appear.

1. There are several thin battens, the lengths of which are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and1cm respectively. The number is sufficient, and three battens can be properly selected as three sides. If the base is 1 1 cm, how many different triangles can you enclose?

There are 7 pairs of white gloves, 8 pairs of black gloves and 9 pairs of red gloves in a bag. A child fumbled for gloves from his bag in the dark, one at a time, but he couldn't see the color clearly. In order to ensure that he can touch at least six gloves, he must touch at least () gloves. Gloves are divided into right and left hands, and any two gloves can be made into a pair.

3. A negotiation meeting between Chinese and foreign companies starts at 10 minute, and the wall clock rings (only when it rings at the hour, it will ring several times). During the whole meeting, * * * heard the bell of 14. At the end of the meeting, the hour hand and the minute hand formed a 90-degree angle. Find out when the meeting started and ended, and what time it is now.

1. Because there are enough solutions, repetition is considered; Now the bottom is 1 1. We need to ensure that the sum of the two sides is greater than the third side, so that the sum of the numbers we want to take out is greater than 1 1. The situation is as follows:

The length of one side is 1 1, and the other side may be1~1* *1in total.

The length of one side is 10, and the other side may be 2 ~ 10. There are 9 cases.

……

One side is 6, and the other side can only be 6 * * *1;

When the length of the lower side is less than 6, it is the same as the previous side, so there are1+3+5+7+9+1= 36 kinds of * *.

Consider the worst luck, so that we can only take the first five pairs with the same color, and then three pairs with different colors. If you take another picture, the color of this picture will be the same as that of the three pictures just now, so you should take at least 5×2+3+ 1= 14.

3. Solution Because how many times it rings is 14=2+3+4+5, it rings at 2 o'clock, 3 o'clock, 4 o'clock and 5 o'clock, so 10 minutes later, which means the start time is 1: 50. Finally, the hour hand and the minute hand form a 90-degree angle, so it can be understood that the hour hand and the minute hand form a 90-degree angle a few minutes after 5 o'clock, so we can calculate the answer as10112 =101. (Consider another case, that is, the minute hand crosses the hour hand by 90 degrees for 40 ÷1112).