Today Puzzle #676
Puzzle No. 676 鈥� Friday 14 February
Today is Valentine’s Day and you give your valentine a single rose costing £15. The sale price for roses decreases by £1 every subsequent day in February and you decide to give your valentine a bunch of roses every day for the rest of the month. If the bunch size increases by one each day, which day will cost you the most?
Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Fellow of Girton College
Click here for the answer
21 February is the most expensive day and will cost you £64, 8 roses at £8 each. You can determine this by going through the remaining days in February and calculating each day. Alternatively, you could note that cost C for each day n after the current one is given by C = (15-n) x (n+1) and see that the mid-point is going to be the most expensive. If you wish to do this by yet another method, you can seek the value of n for which the cost C is a maximum by noting that dC/dn=0 at this point. Expanding out the formula we find C=14n-n2. dC/dn=14-2n and so for dC/dn=0 we see that n=7. The date is therefore Feb 14(today’s date) + 7 = Feb 21.
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