2850.21 – Situps

Your friend Demetrious wants to make the team. To do that he'll have to do 71 situps for the coach, a week from today. Demetrious decides, sensibly, to work up to it. But, being the kind of guy he is, he makes an interesting plan. He will start by doing 3 situps today (no sense rushing into things), and will end on the 7th day with 71. (This will get him his 71 a day early, if you're paying attention.)

Here's his plan: He'll do 3 situps today, a certain number tomorrow, and then starting on the 3rd day the number of situps he does will be the sum of what he did on the two preceding days.

For instance, if today is Friday and he starts with 3 situps, he'll do some situps on Saturday, and on Sunday he'll do the sum of Friday's and Saturday's. Question: How many situps should he do tomorrow (the second day) to come out with 71 on the 7th day?

Solution

Demetrious's situp regime will be 3,x,_,_,_,_,713, x, \_, \_, \_, \_, 71.

Filing in the blanks, we'll have 3,x,3+x,3+2x,6+3x,9+5x,713, x, 3+x, 3+2x, 6+3x, 9+5x, 71.

And that 71 would equal 15+8x15 + 8x. So 8x=568x = 56 and x=7x = 7. That's what he'll do tomorrow.

The full list is 3,7,10,17,27,44,713, 7, 10, 17, 27, 44, 71. So a week from today he can repeat the required 71 for the coach. But if he wants to impress the coach big-time he could continue his regime and do 44+71=11544 + 71 = 115. Knowing Demetrious, he just might go for it.