A charitable lady met a poor man to whom she gave one cent more than half of what she had in her purse. The poor fellow, who was a member of the United Mendicants' Association, managed, while tendering his thanks, to chalk the organization's sign of "a good thing" to her clothing. As a result, she met many objects of charity as she proceeded on her journey.
To the second applicant she gave 2 cents more than half of what she had left. To the third beggar she gave three cents more than half of the remainder. She now had one penny left.
How much money did she start out with?
fairly easy, don't know if there is a formula, but after a min or two of trial and error, i came up with the number 42. and that ladies and gentlemen is your answer...42!
ReplyDeletethank you,thank you
if you just reverse from the end and add 3 cents to 1 you get 4 cents. then take that and times it by 2 to get 8. After this add 2 cents to get 10 and then multiply by 2 to get 20 cents. finally add 1 cent to get 21 and times by 2 and you get your answer 42.
ReplyDeleteLet x = amount of cents she has
ReplyDelete1st beggar gave x/2 + 1
therefore she had x/2 - 1 left
2nd beggar gave (x/2 - 1) / 2 + 2
therefore she had (x/2 - 1) / 2 - 2 left
3rd beggar gave [(x/2 - 1) / 2 - 2] / 2 + 3
therefore she had [(x/2 - 1) / 2 - 2] / 2 - 3 left
thus [(x/2 - 1) / 2 - 2] / 2 - 3 = 1
with simple algebra, we find that x = $42
- t_tactics