Someone needed help with the following question:
The digits 1, 2, 3, 4 and 5 can form 120 five-digit numbers, each without any repeating digit. What is the sum of these 120 numbers?
Solution by Lim Li:
Each of the digits 1, 2, 3, 4 and 5 appears 24 (i.e. 120/5) times in the Ones, Tens, Hundreds, Thousands and 10 Thousands place.
1+2+3+4+5 = 15
24 x 15 = 360
Hence,
+++++360
++++360
+++360
++360
+360
------------
=3999960 (sum of all 120 numbers)
------------
Thursday, 27 January 2011
Tuesday, 25 January 2011
Mathlinks aka Art of Problem Solving
This is posted by LJ's mum.
Mathlinks is a website/forum that Lim Jeck frequents, on an almost daily basis. It is where he hones his Maths Olympiad problem solving skills. Since joining Mathlinks on 10 March 2010, he has contributed 760 posts (as at 25 January 2011) which works out to an average of 2.73 posts per day. Out of a total of 78,927 members, Lim Jeck aka oneplusone is currently ranked the 455th most active user. The most active user has to-date made 12,301 posts in the various forums!
He also participates in an unofficial Olympiad Marathon initiated by a fellow forum user. Currently, he is ranked 1st, after some 14 rounds of questions.
Mathlinks is a website/forum that Lim Jeck frequents, on an almost daily basis. It is where he hones his Maths Olympiad problem solving skills. Since joining Mathlinks on 10 March 2010, he has contributed 760 posts (as at 25 January 2011) which works out to an average of 2.73 posts per day. Out of a total of 78,927 members, Lim Jeck aka oneplusone is currently ranked the 455th most active user. The most active user has to-date made 12,301 posts in the various forums!
He also participates in an unofficial Olympiad Marathon initiated by a fellow forum user. Currently, he is ranked 1st, after some 14 rounds of questions.
Sunday, 23 January 2011
Cut the Rope HD (iPad game)
We are currently the top in national and local for the Cut the Rope game in Cardboard, Fabric and Foil box leaderboard categories, with scores of 140240, 137120 and 132890 respectively.Cut the Rope is a strategic game that tests your puzzle solving skills. There is this cute fat round green monster, Om Nom, who has a penchant for candy. The objective of the game is to bring the candy to Om Nom's mouth which is almost as big as him. If the candy is attached to a rope, you can "Cut the Rope" with your finger. To complete a level, you need to decide which ropes and when to cut, to swing/drop/float/etc the candy into his mouth, collecting as many stars as possible in the process.
We have aready completed the game and have nothing much to do as I am too "sian" to achieve national tops for the gift and cosmic box.
Sunday, 16 January 2011
Funny Photos from Newspapers
Professional Photography?!
From The Straits Times - Feng Tianwei, who rescued Singapore from quarter-final exit during the Asian Games 2010.
From My Paper - Monaco's Princess Stephanie was in Singapore to support her daughter, who participated in the inaugural YOG 2010.
From The Straits Times - Feng Tianwei, who rescued Singapore from quarter-final exit during the Asian Games 2010.
From My Paper - Monaco's Princess Stephanie was in Singapore to support her daughter, who participated in the inaugural YOG 2010.
Saturday, 8 January 2011
2000th 7-digit Math Question
Someone posted the following question:
All the 7-digit numbers containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5, are arranged in the increasing order. Find the 2000th number in this list.
Solved by Lim Li ☺☻:
Since the 7-digit number cannot be divisible by 5, the last digit cannot be 5.
If the 1st digit is fixed, there are 1x2x3x4x5x5 = 600 numbers
[1]765432 => 600th number
[2]765431 => 1200th
[3]765421 => 1800th
If the 1st and 2nd digits are fixed, there are 1x2x3x4x4 = 96 numbers
[41]76532 => 1896th
[42]76531 => 1992nd
:
[4312]756 => 1996th
[4315]267 => 1997th
[4315]276 => 1998th
[4315]627 => 1999th
[4315]672 => 2000th
Hence the 2000th number is 4315672
All the 7-digit numbers containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5, are arranged in the increasing order. Find the 2000th number in this list.
Solved by Lim Li ☺☻:
Since the 7-digit number cannot be divisible by 5, the last digit cannot be 5.
If the 1st digit is fixed, there are 1x2x3x4x5x5 = 600 numbers
[1]765432 => 600th number
[2]765431 => 1200th
[3]765421 => 1800th
If the 1st and 2nd digits are fixed, there are 1x2x3x4x4 = 96 numbers
[41]76532 => 1896th
[42]76531 => 1992nd
:
[4312]756 => 1996th
[4315]267 => 1997th
[4315]276 => 1998th
[4315]627 => 1999th
[4315]672 => 2000th
Hence the 2000th number is 4315672