9747 /www/nrich/html/content/id/9747/ 1 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div style="text-align: center;"><mdo:image src="small%20dice.jpg"></mdo:image></div> <div>I&#39;ve made this model out of dice. It represents an old steam train. Most of the train is blue but there is a white funnel on the engine at the front.<br></br> The dice are put together with the rule that "faces that touch each other have the same number."<br></br> So, underneath the white dice is a $3$ touching a $3$ on the blue dice. That blue dice has a $6$ on the face that touches the $6$ on the middle blue dice. The middle blue dice has a $1$ that touches the $1$ on the last dice.<br></br> You can made models like this one but you could make it the same length or longer, (not shorter) but each one you make is to have the funnel on top of the front dice.<br></br> You have to obey the same rule about faces that touch each other having a same number.<br></br> <br></br> <strong>BUT</strong> AN EXTRA RULE THAT STATES;</div> <div style="text-align: center;">THE NUMBER ON TOP OF THE FUNNEL MUST EQUAL THE TOTAL<br></br> OF THE NUMBERS SHOWING ON TOP OF THE REMAINING DICE (CARRIAGES).<br></br>  </div> <div>AS you can see in my example the $4$ on top of the funnel equals the two $2$&#39;s on top of the blue carriages</div></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">A number of dice making a train with an engine and funnel<br></br> Dice joining with the rule of same-ness ie. four facing four.<br></br> The top of the funnel must equal the addition of 2 or more carriages (dice).<br></br> If 1 or 6 facing then possible ‘tops’ are 2, 3, 4, 5     a<br></br> If 2 or 5 facing then possible ‘tops’ are 1, 3, 4, 6     b<br></br> If 3 or 4  facing then possible ‘tops’ are 1, 2, 5, 6    c <div style="text-align: center;"><mdo:image src="dicetrain%20sol.jpg"></mdo:image></div> <br></br> <br></br></mdoxml> 2 4 0 1 0 0 0