All About Math Olympiad Training & Questions

[Pen88n]

Let me try to get the answers:


1) Between 1 - 99, total # of digits 189 digits
Betweem 100 - 199, total # of digits 300
Between 200 - 299, total # of digits 300
Between 300 - 399, total # of digits 300

So you can see the 1000th digit falls within number "370" and it ends at digit 3.

2) From 1- 100, there are 19 numbers with digit 2 (10 from the "20 - 29" range and 1 each from the "1 - 90 exclude 20+" range)

For 200 - 299, there are 100 numbers with digit 2

From 1 - 1000, there are 100 + 9(19) = 271 numbers with digit 2.

From 1001 - 1999, there are 271 numbers with digit 2

From 2000 - 2009, there are 10 numbers with digit 2

From 1 - 2009, total 271+271+10 = 552 numbers with digit 2

3) 22+24+26+…+200 = 200(200+2)/2 = 20200

Please advise if answers are correct. Thanks

[Courage]

Pen88n, Thanks for your reply.


My working for Q3 is

2(11+12+13+…+100)
2(1+2+3+4+5+…+100)

Using the formula,
1+2+3+4+…+100 is 100(100+1)/2 =5050

thus, 2(5050-55)=9990 since 1+2+3…+10=55

[kiasiparent]

Pen88n:

Let me try to get the answers:


1) Between 1 - 99, total # of digits 189 digits
Betweem 100 - 199, total # of digits 300
Between 200 - 299, total # of digits 300
Between 300 - 399, total # of digits 300

So you can see the 1000th digit falls within number \"370\" and it ends at digit 3.

2) From 1- 100, there are 19 numbers with digit 2 (10 from the \"20 - 29\" range and 1 each from the \"1 - 90 exclude 20+\" range)

For 200 - 299, there are 100 numbers with digit 2

From 1 - 1000, there are 100 + 9(19) = 271 numbers with digit 2.

From 1001 - 1999, there are 271 numbers with digit 2

From 2000 - 2009, there are 10 numbers with digit 2

From 1 - 2009, total 271+271+10 = 552 numbers with digit 2

3) 22+24+26+....+200 = 200(200+2)/2 = 20200

Please advise if answers are correct. Thanks

First 2 are correct
3) 45 pairs x 222 = 9990

[Pen88n]

Thanks, Courage & Kiasiparent.


Finally see \"light\" for Q3.

It's great workout for my brain

[Tang]

Pen88n:

Let me try to get the answers:


1) Between 1 - 99, total # of digits 189 digits
Betweem 100 - 199, total # of digits 300
Between 200 - 299, total # of digits 300
Between 300 - 399, total # of digits 300

So you can see the 1000th digit falls within number \"370\" and it ends at digit 3.

2) From 1- 100, there are 19 numbers with digit 2 (10 from the \"20 - 29\" range and 1 each from the \"1 - 90 exclude 20+\" range)

For 200 - 299, there are 100 numbers with digit 2

From 1 - 1000, there are 100 + 9(19) = 271 numbers with digit 2.

From 1001 - 1999, there are 271 numbers with digit 2

From 2000 - 2009, there are 10 numbers with digit 2

From 1 - 2009, total 271+271+10 = 552 numbers with digit 2

3) 22+24+26+....+200 = 200(200+2)/2 = 20200

Please advise if answers are correct. Thanks

1)
1 to 9 --> 9 digits
10 to 99 --> 2 x 90 = 180 digits
100 to 299 --> 3 x 200 = 600 digits

1000 - 9 - 180 - 600 = 211 digits

211 / 3 = 70 r 1 --> So number from 300 to 369 and 3(70) is incomplete
Hence the digit is 3.

3)
(2 + 4 + .... 200) - (2 + 4 + ....20)
= (2+200)/2 x 100 - (2+20)/2 x 10
= 10100 - 110
= 9990

[mathzgenius]

Courage:

Need :?: for the following questions:


(1) If we write whole numbers starting from 1 to form a 1000-digit number N as follows: N=12345678910111213.... what is the unit digit of N?

(2) How many whole numbers from 1 to 2009 contain the digit \"2\"?

(3) Study the following pattern:

1=1: 1(1+1)/2=1
1+2=3; 2(2+1)/2=3
1+2+3=6; 3(3+1)/2=6
1+2+3+4=10; 4(4+1)/2=10
1+2+3+4+5=15; 5(5+1)/2=15

Find the value of 22+24+26+....+200.

TIA.

My answers for the questions are:

2)355

3)55

Please advise if the answers are correct. I can teach you how to work it out mentally.

* How do you solve Q1??

Please help. I don't quite get your workings. TIA

[Merlion]

> 3)55


How can 22+24+ … +200 equal to 55? No way.
We can simply use Gauss’s method, the answer is 9990.

[Tang]

Merlion:

> 3)55


How can 22+24+ .... +200 equal to 55? No way.
We can simply use Gauss's method, the answer is 9990.

(2 + 4 + ...... + 200) - (2 + 4 + ..... + 20)
= (2 + 200)/2 x 100 - (2 + 20)/2 x 10
= 10100 - 110
= 9990

[kidsjoy]

Maths Olympiad is hot here. Myself went through this training and loved it. Also it helped prepare me in logic and analysis that helps a lot in my higher education. But as said by some parents here, I am born to have a stronger mind in this type of analysis. Well, I am really weak in art . I did spent some time looking around, and I do not find lots of this type of training in Singapore. Looks like only the school themselves have these training. Anyway, still a long way for my kids.

[usaik]

Please pardon my ignorance. I was trying to look for maths enrichment class information for my P2 kiddo and happen to stumble into this thread. After browsing through the thread. I am still not very sure what is the purpose of Maths Olympiad?


What is the purpose of so many parents sending their kids for Maths Olympiad training?

Why is the objective of the Olympiad competition? What are the schools trying to achieve?
[quote]Maths Olympiad is hot here. Myself went through this training and loved it. Also it helped prepare me in logic and analysis that helps a lot in my higher education. But as said by some parents here, I am born to have a stronger mind in this type of analysis. ..[/quote] Hi Kidsjoy, you make the training sound fun..... can share whether it help to do well in the school Maths syllabus by attending this FUN training? THANKS!