6223 /www/nrich/html/content/id/6223/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p>Our school dinners offer the same basic choice each day.<br></br> <br></br> <span style="font-style: italic;">Starters:</span> soup or fruit juice;<br></br> <span style="font-style: italic;">Main course:</span> meat, fish, salad, chicken or curry;<br></br> <span style="font-style: italic;">Afters:</span> crumble, cake or sponge<br></br> <br></br> I change my choice for each course every day, trying each option in turn, going back to soup after fruit juice, to meat after curry and to crumble after sponge. Today, I shall sit down to soup, meat and crumble.</p> <p>How many school dinners will I have eaten before I next sit down to the same combination?</p> <p> </p> <p>If you liked this problem, <a href="http://nrich.maths.org/6650">here is an NRICH task</a> which challenges you to use similar mathematical ideas.</p> <p> </p> <p> </p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> Every second meal I will have soup for my starter.<br></br> Every $5$th meal I will have meat for my main course.<br></br> Every $3$rd meal I will have crumble for my afters.<br></br> <br></br> $2, 5$, and $3$ have no common factors, so I will have eaten $2\times5\times3=30$ school dinners before I sit down to the same combination.<br></br></mdoxml> 2 4 0 0 1 0 0 Our school dinners offer the same choice each day. I try each option for each course in turn. Today I shall sit down to soup, meat and crumble. How long will it be before I eat the same meal again? Numbers and the Number System Common factors