**From New Scientist #1788, 28th September 1991** [link]

Rosemary was getting tea for 124 visitors. There were 17 biscuits in each packet, and she wanted to buy a number of packets so that each visitor had the same number of biscuits and there was one biscuit left over for her to have after she had washed up.

Rosemary had a routine for finding the answer. First, she calculated that if each visitor had one biscuit, then she would need 7 packets and 5 extra biscuits. She noted the number 5, and looked at the question of 5 visitors and 17 biscuits in each packet. That was easy — she would buy 3 packets, giving 51 biscuits, so that each visitor had 10 biscuits and there was one left over for her. She noted the number 10, and returned to her original question. She gave each of the 124 visitors 10 biscuits, and adding one more for her gave 1241 biscuits, which is exactly 73 packets.

The next day, Rosemary had 53 visitors and 113 biscuits per packet, but the problem was the same, namely, to have one biscuit left over for her.

Because the number of visitors was less than the number of biscuits, she had to include an extra routine. First, she changed to the question of 113 visitors and 53 biscuits per packet. Now she could use her first-day routine, and she found the answer was 32 packets and 15 biscuits per visitor. Next she subtracted the 32 from the 113 to get 81, and the 15 from the 53 to get 38. Then the original question of 53 visitors and 113 biscuits per packet had its answer: 38 packets and 81 biscuits per person.

On the third day, Rosemary had 293 visitors and 119 biscuits per packet. Again, she wanted to buy a number of packets so that each visitor had the same number of biscuits and there was one left over for her. Also, for the visitors’ health, she decided that each one should get less than a packet.

Either by using Rosemary’s routine, or by your own method, calculate the number of packets she should buy on the third day.

#### News

This brings the total number of **Enigma** puzzles on the site to 1,500 (with 292 puzzles remaining to post), nearly 84% of all **Enigma** puzzle published in *New Scientist*.

For the past year or so I have endeavoured to post 7 puzzles a week between **Enigmatic Code** and **S2T2**, so that people who have found themselves with time on their hands because of the pandemic are not at a loose end. However I now find that I need to make time for other things, so I don’t expect to maintain this posting frequency in the future.

However, there are now 2,381 puzzles available between the two sites, so I hope there are enough for people to keep people amused for the time being. (They are weekly puzzles, so that is over 45 years worth).

Happy Puzzling!

[enigma634]

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