Twelve Days of Christmas GiftsDate: 12/06/2001 at 18:26:25 From: Katie Subject: 7th grade math How many presents did the person receive in the song "The 12 Days of Christmas"? Date: 12/07/2001 at 15:58:16 From: Doctor Ian Subject: Re: 7th grade math Hi Katie, On the first day, there is one gift: 1 On the second day, there is another one of that gift, and two more: 1 1 2 On the third day, 1 1 2 1 2 3 and so on, up to 12 days: 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 ^ ^ ^ | | | | | +---------------------------- 10 * 3 | +------------------------------ 11 * 2 +-------------------------------- 12 * 1 So that's 12*1 + 11*2 + 10*3 + 9*4 + ... 4*9 + 3*10 + 2*11 + 1*12 Note that some of the terms are the same: 12*1 + 11*2 + 10*3 + 9*4 + ... 4*9 + 3*10 + 2*11 + 1*12 \ \ \ \_________/ / / / \ \ \___________________/ / / \ \_______________________________/ / \___________________________________________/ That's convenient, because it means you only have to add up half the terms: 2 * [12*1 + 11*2 + 10*3 + 9*4 * 8*5 * 7*6] Can you take it from here? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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