Finish this sequence:
10, 11, 12, 13, 14, 21, 100, 1001
This one is also fun. What comes next in this sequence:
1, 11, 21, 1211, 111221
Chill Out Area : math problem
 SeaHorseRacing
 Posts: 1898
 Joined: Fri May 20, 2016 7:06 pm
As the racing is so crap.
Answer 1 = 10002
Answer 2= 312211
Answer 1 = 10002
Answer 2= 312211
yeah, agreed pretty crap racing, so google to the rescue:SeaHorseRacing wrote:As the racing is so crap.
Answer 1 = 10002
Answer 2= 312211
https://oeis.org/A001731 (111111111 is next here mind you!!)
https://en.wikipedia.org/wiki/Lookandsay_sequence
 marksmeets302
 Posts: 481
 Joined: Thu Dec 10, 2009 4:37 pm
Yep, the first sequence is all nines, but in different bases. 10 = 9 in base 9, 11 is 9 in base 8 etc. 111111111 is 9 in base 1.
For the second sequence: 11 is pronounced as "2 ones", therefore the next in line 21. This is read as "1 two and 1 one", so the next one is 1211, etc.
For the second sequence: 11 is pronounced as "2 ones", therefore the next in line 21. This is read as "1 two and 1 one", so the next one is 1211, etc.
Not a maths puzzle per se, but actually a maths family heirloom passed down from my father to me and subsequently to my 4 kids.
This little visual formula works on the mysterious qualities of the multiplier of 11 (eleven). Basically, I introduced it to my own kids by asking them to write down 5 random 3 or 4 figure numbers on a piece of paper and then told them to grab a calculator. My challenge was then for them to write down the value of the random numbers on the sheet when multiplied by 11 before I verbally announced the results of each. I of course won every time as the mystical visual maths when using 11 is actually pretty straightfwd.
Here is a typical example of the random numbers that I would be challenged with:
453, 1427, 4263, 363, 906 (etc..)
I would of course instantly (in those days!!) respond with:
4983, 15697, 46893, 3993, 9966
They thought I was some kind of savant until I explained the *secret* behind this wizardry. It's just a simple case of adding the digits of all the sequence together to form the result as follows:
1427 * 11 = 15697 (take the 1st digit of the challenge number [1], then, add together each pair of adjacent digits and append the last digit to finalize)
i.e. 1 followed by 1st + 2nd(5), 2nd + 3rd(6) and 3rd + 4th(9). finally, take the last digit (7) and put it on the end of the result.
Hopefully, you get the gist and will borrow this as your family maths heirloom
Caveat  in order to keep this little puzzle simple, always ensure that adjacent digits add up to no more than 9, otherwise you have to do some further mental add and carry arithmetic; ok if you're sub 35, not nowadays alas
This little visual formula works on the mysterious qualities of the multiplier of 11 (eleven). Basically, I introduced it to my own kids by asking them to write down 5 random 3 or 4 figure numbers on a piece of paper and then told them to grab a calculator. My challenge was then for them to write down the value of the random numbers on the sheet when multiplied by 11 before I verbally announced the results of each. I of course won every time as the mystical visual maths when using 11 is actually pretty straightfwd.
Here is a typical example of the random numbers that I would be challenged with:
453, 1427, 4263, 363, 906 (etc..)
I would of course instantly (in those days!!) respond with:
4983, 15697, 46893, 3993, 9966
They thought I was some kind of savant until I explained the *secret* behind this wizardry. It's just a simple case of adding the digits of all the sequence together to form the result as follows:
1427 * 11 = 15697 (take the 1st digit of the challenge number [1], then, add together each pair of adjacent digits and append the last digit to finalize)
i.e. 1 followed by 1st + 2nd(5), 2nd + 3rd(6) and 3rd + 4th(9). finally, take the last digit (7) and put it on the end of the result.
Hopefully, you get the gist and will borrow this as your family maths heirloom
Caveat  in order to keep this little puzzle simple, always ensure that adjacent digits add up to no more than 9, otherwise you have to do some further mental add and carry arithmetic; ok if you're sub 35, not nowadays alas
 marksmeets302
 Posts: 481
 Joined: Thu Dec 10, 2009 4:37 pm
I got this one from the dutch financial times. When I checked my answer I found that they had an amazingly elegant solution.
Tomorrow is Blue Monday, that day of the year when we are on average most depressed. There are 20 people in a street and nobody wants to meet with another. Whenever two persons are about to meet each other they both just turn around and walk in the opposite direction. It takes 10 minutes to walk the entire street and people start in random positions. What is the maximum time it takes before everybody has cleared the street?
Tomorrow is Blue Monday, that day of the year when we are on average most depressed. There are 20 people in a street and nobody wants to meet with another. Whenever two persons are about to meet each other they both just turn around and walk in the opposite direction. It takes 10 minutes to walk the entire street and people start in random positions. What is the maximum time it takes before everybody has cleared the street?

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