Whats the easy way of finding a total?

[banana]

A quiz night question was - how many presents in total were given in the 12 days song? We had to do it the slow way , but Im sure there must be an alogrithm or other quick method of doing this calculation.Any ideas?

[woofgang]

six times thirteen

[shybearuk]

Woofgang is right, but the formula is: smallest number plus largest number (1+12=13) multiplied by half the number of 'sets' (12/2=6). For an odd number you will obviously get a half somewhere in here, but it should still work.. This should work for any series of consecutive numbers. I just worked this out now, so if I am wrong in this, I shall slink away to my corner....

[jenstar]

However... it doesn't help with the total number of presents given. The narrator of the song gets a partridge in a peartree on each day, so that's 12 gifts (let's go with tradition and assume a partridge and a peartree are a single gift and not two separate ones). Pus 11x2 turtledoves, 10x3 french hens, 9x4 colly birds... well, you get the picture.

[banana]

Wolfgang and Shybear ,you were both at the point where we were -before we realised that the total for every days presents was needed. Jenstar - thats a different way to how we did it.We had totalled cumulatively ( 1+3+6+10 etc ) but it was slow and prone to errors ( took about 6 goes before we both agreed).Ive looked on google but nothing has come up.I was thinking of something like 12 factorial ( but obviously not that exactly).Perhaps an easy way doesnt exist !

[davver]

woofgang and shybear, I'm not sure how you get to 364 with that! 6x13 is 78. I also had it in a pub quiz, and just did 1x12 + 2x11 + 3x10... etc. Of course, you only have to do half and then multiply by two because the two halves are identical. But banana, I'm sure you're right about there being another way, a formula, because I dimly remember doing something like this for A-level all those years ago.

[lisaj]

easy. total=0; numberofdays=12; foreach numberofdays as thisdaynumber { total += sum(0 to thisdaynumber); } print total;

[emandvee]

I must be a bit of a simpleton, but I just added up 1 through 12 and it came to 80, BUT was this the correct answer?

[emandvee]

Whoops....78

[davver]

Don't forget, Marj, that each day not only does the recipient get the present for that day, but a reapeat of each of the previous days a well. E.g., on the 3rd day he receives 3 French hens, two turtle doves and a partridge in a pear tree. This adds to the two turtle doves and the two partidges in pear trees that he already has, having received them on days one and two. I hope that's clear!

[5029]

The correct answer is in fact 364, not sure if there is a *simple* formula for working this out though, good luck!