Question 4
A shop sells two types of buns, with either cream or jam filling, which are indistinguishable until someone bites into the buns. Four mathematicians visited the shop and ordered (not necessarily in that sequence): three cream buns, two cream buns and one jam bun, one cream and two jam buns, and three jam buns. Each knew precisely what the others had ordered. Unfortunately, the shop owner mixed up the orders and gave each mathematician the wrong order!
The mathematicians started eating, all still unaware of the mixup, until the shop owner came over to inform them of the mistake. Mathematician A said: “I ate two buns and both had cream filling. So, if my order was wrong, I now know what type my third bun is.” Mathematician B then said: “I only ate one bun and it had cream filling. Based on what A said and since I remember A’s order, I now know what type my other two buns are.” Finally, Mathematician C said: “I have not started eating but I must have received three jam buns.” Which of the following statements about Mathematician D is correct?
The mathematicians started eating, all still unaware of the mixup, until the shop owner came over to inform them of the mistake. Mathematician A said: “I ate two buns and both had cream filling. So, if my order was wrong, I now know what type my third bun is.” Mathematician B then said: “I only ate one bun and it had cream filling. Based on what A said and since I remember A’s order, I now know what type my other two buns are.” Finally, Mathematician C said: “I have not started eating but I must have received three jam buns.” Which of the following statements about Mathematician D is correct?