# Movie Ticket Puzzle Solution

[This is a back-issue of one of this site’s newsletters]

It’s Monday Morning Math Time!

If you’re hungry, have a look at this yummy breakfast math video. You’ll see there’s more than one way to cut a bagel, and maybe learn a bit of topology too.

I promised to give you a solution to the movie ticket problem.
If you missed it, have a read here and see if you can solve it before you read on here!

So, adults tickets cost \$16, child tickets cost \$8. If you use the “four tickets for \$11” voucher, you pay \$44, but if you use the 10% off voucher, it only costs \$43.20. The latter is clearly better, and you have \$6.80 in your wallet for popcorn.

However, you can do better than that. If you use the \$11 voucher for the two adult tickets only, then use the 10% voucher for the kids’ tickets, you only pay \$34.40. Now, the voucher says “four tickets at \$11 each”, it doesn’t say you’re allowed to buy only two. However, you can always turn to the family behind you in the line, and say to mom and dad “How’d you like to pay only \$11 for your two tickets?”

Actually, you can do even better than that. You could buy four adult tickets for \$11 each, and the two kids’ tickets for \$7.20 each, then try to scalp two of the adult tickets. If you’re really lucky, you can sell them to someone at the back of the line for full price. Then, the four adult tickets cost \$44, you sold two for \$32, and then the two kids’ tickets were \$7.20 each. You’ve spent \$26.40.

However, since you’re scalping tickets now, why not sell all four of the adult tickets? Then, you can buy your family’s four tickets using the 10% voucher. Your costs are: \$44 for the tickets you sell, \$43.20 for the tickets you use. That’s a total of \$87.20. If you sell four adult tickets for \$64, you’ve got into the cinema for only \$23.20.

This is just casual ticket scalping though. After flogging off the first four tickets, you have enough money in your wallet to buy four adult tickets using the 10% discount voucher – or, if you can borrow two bucks from one of the kids, five tickets for \$72. Selling these nets you another \$8 profit. Of course, you now have no vouchers, so you have to buy your family’s tickets at full price, but (after returning your child’s two dollar “investment”), you’ve managed to get everyone into the cinema for only \$20. Thirty bucks can buy a lot of popcorn.

Some say scalping is unscrupulous. If you’ve already compromised your scruples, you can always compromise them further as suggested by one correspondent: Buy four adult tickets for \$44, and sell then for \$64. Then, buy four adult tickets and one child ticket using the 10% voucher, for \$64.80. Sell the adult tickets for \$64. So far, you’ve made a profit of \$19.20. Then, send the child into the cinema, with instructions to quietly let you in through the fire exit. Now, you’re in the cinema, watching the movie, with \$69.20 worth of popcorn and a guilty conscience. That’s a heavy bag of popcorn. And conscience.

Of course, if the cinema gets wind of these shenanigans, you may be forced to use a different kind of creative answer: “Your vouchers have expired, and you must pay the full price of \$48.”

That’s all for this week, don’t forget to keep thinking about the time machine puzzle. Oh, and if you’re looking for an Advent Calendar, my website has one you can download and print.

Enjoy!