Puzzles with numbers and things

[davis_greatest]

SO HERE IS THE SCOREBOARD AFTER ROUND 90 BUT BEFORE ROUNDS 88 AND 91

snookersfun………....………….…..44½
abextra...............................28
davis_greatest.....................21
Vidas..................................12½
chasmmi..............................10
elvaago...............................10
Sarmu..................................8
robert602.............................7
The Statman…………………. …...…5
Semih_Sayginer.....................2½
austrian_girl and her dad.........2½
Snooker Rocks! .....................2
Ginger_Freak.........................1½
April Madness........................1

[elvaago]

At least give us the answer!

[snookersfun]

OK, I'll give out points already for my round, as I don't really expect any more input. (but whoever is still brainstorming has another 40 mins to do so)
Abextra just squeezed in an answer for n=7, therefore she'll get one point. Well done
Now d_g with his neat program, a bid of 80 (or even more, can't remember) plus the perfect explanation above deserves 2 points!

So, d_g, if you have time to update, otherwise, I'll do it later on.

[Snooker Rocks!]

Oh of course

My apologies, the answer was 364 (elvaago, close but no cigar )

[davis_greatest]

Oh of course

My apologies, the answer was 364 (elvaago, close but no cigar )

As Snooker Rocks! will tell us, after n days of Christmas you have n(n+1)(n+2)/6 pressies (the nth tetrahedral number!). Put n=12 and you get the 364.

[elvaago]

Ah crap, I typoed my final answer.

[Snooker Rocks!]

As Snooker Rocks! will tell us, after n days of Christmas you have n(n+1)(n+2)/6 pressies (the nth tetrahedral number!). Put n=12 and you get the 364.

Yes, that's right.

Fundementally, you should have noticed that the presents each day, were the term of the triangular sequence, with each day being the term number.

Knowing this, you could either use the forumla for the nth tetrahedral number, and then work out the 12th term, which would give you the total pressies,

OR, knowing that it is just the sum of the first twelve triangular numbers, you could have simply used sigma and the formula for the nth triangular number:

[snookersfun]

deadline definitely passed now. Chasmmi jumped in as well (a bit late, but he is in Seoul and it is Christmas)
SO HERE IS THE SCOREBOARD AFTER ROUND 88 BUT BEFORE ROUND 91

snookersfun.........................44½
abextra...............................29
davis_greatest.....................23
Vidas..................................12½
chasmmi..............................11
elvaago...............................10
Sarmu..................................8
robert602.............................7
The Statman.........................5
Semih_Sayginer.....................2½
austrian_girl and her dad.........2½
Snooker Rocks! .....................2
Ginger_Freak.........................1½
April Madness........................1

[snookersfun]

oh, and here is Abextra's number:
7 3 6 2 5 3 2 4 7 6 5 1 4 1

and, I am adding a solution for 8 from Chasmmi, who is in Seoul and doesn't know, what is the time here... so, in the Christmas spirit, have a point as well very nice!

7 8 2 3 6 2 5 3 7 4 8 6 5 1 4 1


and here is a solution for 20 numbers done with d_g's program:
20,18,19,15,11,17,10,16,9,5,14,1,13,1,12,5,11,10,9 ,15,18,20,19,17,16,14,13,12,8,4,7,3,6,2,4,3,2,8,7, 6

he might want to put up his highest number solution later on...

[Snooker Rocks!]

ROUND 92:

In algebraic terms what is the area of this triangle?

If it helps you, this is an equilateral triangle.

ANSWERS BY PM PLEASE. DEADLINE 20:00 SUN. 25TH

[chasmmi]

hooray I gots me a point again

[davis_greatest]

Yes, that's right.

Fundementally, you should have noticed that the presents each day, were the term of the triangular sequence, with each day being the term number.

Knowing this, you could either use the forumla for the nth tetrahedral number, and then work out the 12th term, which would give you the total pressies,

OR, knowing that it is just the sum of the first twelve triangular numbers, you could have simply used sigma and the formula for the nth triangular number:

By the way, if you sum that expression you put up, using the facts that:

- the sum of the first n numbers (i.e. 1+2+3+...+n) is n(n+1)/2; and -
- the sum of the first n squares is n(n+1)(2n+1)/6,

that's how you get the result n(n+1)(n+2)/6 for the nth tetrahedral number.

[lagermike]

Davis greatest ever type character,

What are you getting from the bearded guy this year? The snooker fan's guide to calculus perhaps?

[April madness]

Mike, why does he need that? He knows all that stuff already

[lagermike]

Mike, why does he need that? He knows all that stuff already

Yes Maruta, just a thought. I bet it's not as warm in Riga as it was in August!!