Kangaroo Math question

sebsam

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Hi, I'm studying for Kangaroo Math, and this is a question from the 2010 test:

30.) A magical kingdom is inhabited by dragons with six, seven, and eight heads. Those with 7 heads always lie, and those with 6 or 8 heads always tell the truth. One day four dragons met. The blue dragon said, "Together we have 28 heads," the green dragon said, "Together we have 27 heads," the yellow dragon said, "Together we have 26 heads," and the red dragon said, "Together we have 25 heads." What color was the dragon that did not lie?

ok, so the answer is: the green dragon, who said we have 27 heads. But I can't figure out why this is the answer?

As far as I can tell, 28 heads can be made up of both only 6s and 8s, or a combination that includes 7s, as can 26 heads. 27 heads and 25 heads can only be made up of combinations that include 7s ... I keep trying different combinations, but can't figure out why it's the green dragon, if the one with 7 heads always lies... help?

Thank you so much if anyone can help lead me in the right direction!
 
Hi, I'm studying for Kangaroo Math, and this is a question from the 2010 test:

30.) A magical kingdom is inhabited by dragons with six, seven, and eight heads. Those with 7 heads always lie, and those with 6 or 8 heads always tell the truth. One day four dragons met. The blue dragon said, "Together we have 28 heads," the green dragon said, "Together we have 27 heads," the yellow dragon said, "Together we have 26 heads," and the red dragon said, "Together we have 25 heads." What color was the dragon that did not lie?

ok, so the answer is: the green dragon, who said we have 27 heads. But I can't figure out why this is the answer?

As far as I can tell, 28 heads can be made up of both only 6s and 8s, or a combination that includes 7s, as can 26 heads. 27 heads and 25 heads can only be made up of combinations that include 7s ... I keep trying different combinations, but can't figure out why it's the green dragon, if the one with 7 heads always lies... help?

Thank you so much if anyone can help lead me in the right direction!

The dragons gave four different answers, so we know right away that either three or all four were lying. But then the problem tells us that one of them wasn't lying: " What color was the dragon that did not lie?" Therefore, we know there are three liars and one truthful dragon.

Three liars equals 21 heads (3 times 7). The truthful dragon had either 6 or 8 heads, so possible totals would be 27 or 29. However, no dragon said 29 heads, so 27 is the answer.
 
oh! that was so much easier than I was making it. Thank you sooo much!!!!
Best,
sebsam
 
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