# Dragon lizards in Hogwarts

Albus Dumbledore keeps 274 dragon lizards in his terrarium in Hogwarts. One day he removes two thirds of the male lizards from the terrarium; it is easy for him to tell the males apart from the females since each male has 12 spikes and each female has 4 spikes. How many spikes are left in the terrarium?

• It's a trick question, because one of the male lizards left in the terrarium is named "Spike". Commented Mar 5, 2015 at 17:40
• Why not Blast-Ended Skrewts? Commented Mar 5, 2015 at 21:50

## 2 Answers

There are exactly

1096 spikes left. It doesn't matter how many males or females there are, because the males have 3 times as many spikes as the females. 1/3 of the males remain, and all of the females remain. This averages to 4 spikes per original dragon lizard, which give us 274*4=1096.

• Wouldn't the 274 in your number be the wrong thing to use? If you want to know how many spikes are left, you can't use that number because that will only lead you to how many spikes there were before he removed the dragon lizards. Commented Mar 5, 2015 at 21:09
• @AndrewCoonce No, his logic is correct. If they were all female, he didn't remove any so 274 is the right number to use. If he removes 2, then there are now 271 females and 1 male, 1 male counts like 3 females, so 274 females worth of spikes are left. Commented Mar 5, 2015 at 21:11
• Ah, I see... well reasoned! Commented Mar 5, 2015 at 21:12

Although mfc32 answer is correct I'd like to add a more mathematical approach:

F = number of females in the beginning
M = number of males in the beginning
S = number of spikes in the end

F + M = 274
S = 4 * F + (1/3) * 12 * M
S = 4 * F + 4 * M
S = 4 * (F + M)
S = 4 * 274 = 1096