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Christmas Puzzles

Dr Tom Crawford, University of Oxford/Tom Rocks Maths

Puzzle 1: Baubles

You have 24 Christmas baubles that you want to arrange in a rectangle. How many different sizes of rectangle can you create?

Difficulty level: * easy

Puzzle 2: Stamps

Christmas stamps are sold with the following values 16p, 17p, 23p, 24p, 39p and 40p. You want to send a present which has a postage cost £1.00. How many stamps do you need to buy to make the exact amount?

Difficulty level: ** intermediate

Puzzle 3: Reindeer and carrots

On Christmas night Santa needs to travel the circumference of the Earth — 24,901 miles — to deliver presents. He has 4 sacks of carrots to feed his reindeer, where each sack contains 10 carrots, giving a total of 40. He must feed 1 carrot per 1000 miles to the reindeer, plus an extra 1 carrot for every sack carried for 5000 miles. Does he have enough carrots to complete his journey?

Difficulty level: *** hard

Scroll down for the answers…

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keep going

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almost there

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ta-dah!

Answers:

Puzzle 1: Baubles

1 x 24, 2 x12, 3 x 8, 4 x 6, 6 x 4, 8 x 3, 12 x 2, 24 x 1
Total = 8 different rectangles

Puzzle 2: Stamps

16 + 16 + 17 + 17 + 17 + 17 = 100

Puzzle 3: Reindeer and carrots

Yes. He starts with 40. After 5000 miles, he has used up 5 for the distance and 4 for carrying the sacks, leaving 31. After the next 5000 miles, another 5 are used for the distance and another 4 for carrying the sacks, leaving 22. For the next 5000 miles, he only has 3 sacks remaining and so a total of 8 carrots are used up, leaving 14. The next 5000 miles require 5 for distance and only 2 for the sacks, leaving 7. He can then travel the last 5000 miles with only 1 sack completing the journey with one carrot remaining.

Author

Dr Tom Crawford — for more maths fun check out Tom’s website tomrocksmaths.com and follow him on Twitter, Facebook, Instagram and YouTube @tomrocksmaths.


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