#198 Christmas candles
set by Paulo Ferro
Your turkey needs exactly 6 hours to slow roast. Alas, you have no timer, just three candles: one that burns in 3 hours, one that burns in 4 hours and another that burns in 5 hours.
How can you measure 6 hours using these candles, putting the roast in the oven at the same time as you light the first candle?
#198 Christmas candles
Solution
Here is one way. Light all three candles. When the 3-hour candle burns out, blow out the 4-hour candle. When the 5-hour candle burns out, relight the 4-hour candle for its final hour.
#199 Sneaking a peek
set by Brian Hobbs
Dear Santa,
I can explain. We weren鈥檛 planning to peek at the gifts Aunt Emily brought us, but the receipt was sticking out of one of the bags and Joe accidentally saw it and accidentally told us, so then we knew she got us all lightsabers, two green and three blue. Edmund wants a blue one and I want green. Timothy said it wouldn鈥檛 really be cheating if we only peeked at the gift of the sibling younger than us, but I said that isn鈥檛 fair because I鈥檓 youngest, so we agreed to look at the gifts of both the siblings younger and older than us, which means I only looked at one and it was only a tiny peek.
After that, Georgia asked if anyone knew what they themselves got, and we all said no, except then she smiled and said that if no one else knew, then she did know. I guess I鈥檒l just have to wait to know what colour mine is. I hope you can still bring me presents and please take the lightsabers off the list I sent you.
Love,
Sophie
What colour was Sophie鈥檚 lightsaber?
#199 Sneaking a peak
Solution
Sophie got a green lightsaber. The only way one of the children could know what colour they had after looking at two gifts is if they saw two green lightsabers, meaning the others would have to be blue. Since no one knows initially, the green ones can鈥檛 be in the gifts of both the first and third children, or the second and fourth or the third and fifth. The only child who would be able to use this information to find out what they had is the third child and only if they saw two blue lightsabers. They would know they didn鈥檛 have green because then the first or fifth child would also have green and the second or fourth child would have seen two greens. So she must have blue, leaving the oldest and youngest children with the green lightsabers.
#200 A picture of elf
set by Katie Steckles
鈥楾was just a few days before Christmas. Santa was out for a revitalising walk on the hills around his workshop with his sleep-deprived elf companion Bubby, when he spied a group of other elves moving around on the next hill. 鈥淎h,鈥� he surmised. 鈥淭hey鈥檙e using their special secret elf communication system that only elves can understand, elf-maphore.鈥� The system involves holding two trees in specified positions to represent a letter of the alphabet.
As they watched, three separate groups of elves ran up to the top of the hill and each group spelled out a different word. 鈥淲hat does the message say?鈥� Santa asked. Bubby flipped her elf hat over to the right, as elves always do when using the language, and squinted her tired eyes at the elves on the far away hill, watching them repeat the message. 鈥淲ell, it appears to say PSTA HERHL LTNORL. But that can鈥檛 be right!鈥�
What is the message?
#200 A picture of elf
Solution
The elf hats are tipped to the right, which means we must be viewing them from behind. The view from the front, showing the true message, will be a reflection of each word we can currently see. For example, the last signal in the first line will be the first letter of the message, but reflected left-to-right; the mirror image of this signal occurs elsewhere in the message, and according to the elf鈥檚 initial translation, gives an H. The whole message reads HELP SANTA SNORES.
#201 A prime Christmas tree
set by Paulo Ferro
Your challenge is to fill each hexagon in the Christmas tree with a different prime number. Each side of the triangle the tree makes must add to the same sum and each line鈥檚 total should be as small as possible. Note that, by convention, 1 isn鈥檛 a prime number.
Answers to the festive puzzles, plus the solutions to 10 December鈥檚 puzzle and crossword, are on page 86
#201 A prime Christmas tree
Solution
3
13 19
17 5 11
#197 Marshmallow test
(set on 10 December) Solution
The solid lines are the full-length cocktail sticks, the dotted lines are the shortened sticks. Two of the sticks cross each other, but the marshmallows are chubby enough that they can still all sit on the table top when this happens.