Parallelogram 10 Level 1 9 Nov 2023Jumping frogs

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. a portmanteau word combining parallel and telegram. A message sent each week by the Parallel Project to bright young mathematicians.
  • Tackle each Parallelogram in one go. Don’t get distracted.
  • Finish by midnight on Sunday if your whole class is doing parallelograms.
  • Your score & answer sheet will appear immediately after you hit SUBMIT.
  • Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.

1. The jumping frog puzzle

Watch this frog puzzle video from Gordon Hamilton, and make sure to pause it and try some of the puzzles.

Hopefully they will leave you jumping for joy, rather than hopping mad!

(If you have problems watching the video, right click to open it in a new window)

1 mark

1.1 How far would a stack of 7 frogs jump?

  • 6 lily pads
  • 7 lily pads
  • 8 lily pads
  • 14 lily pads
  • (Not answered)
2 marks

1.2 Since we can solve the Jumping Frogs puzzle for 2 lily pads and 3 lily pads, which other numbers can be solved in the same way?

  • 30, 60, 90…
  • 9, 27, 81…
  • 36, 216, 1296…
  • all of the above and every other number in the 3 times table
  • (Not answered)

After finding the methods for two and three we can break larger groups of frogs up and consider them as groups of two or three.

e.g. 6 lily pads can be solved by applying the method for three and then for two,

9 lily pads can be solved by applying the method for three, twice.

1 mark

1.3 When the lazy toad and queen frog are introduced, which numbers can be solved?

  • all numbers
  • prime numbers only
  • all integers
  • multiples of three only
  • (Not answered)
2 marks

1.4 It is possible to solve some puzzles with water logged lily pads.

Can you find a solution for this case where the two water logged lily pads are next to each other?

  • Yes, a solution is possible
  • No, in this case there is no solution
  • (Not answered)
Show Hint (–1 mark)
–1 mark

Start at the second frog from the left.

Starting at the second frog from the left we can jump 1 to the right, then two to the left, then three to the left and all frogs are happy partying on the lily pad.

2. More puzzles from the pond

2 marks

2.1 Another classic lily pad puzzle:

If a lilypad in a pond triples in size every day it will take over the whole pond in 42 days.

On which day was it only covering one third of the pond?

  • day 14
  • day 41
  • day 7
  • day 6
  • (Not answered)

Since the lily pad triples in size evey day if it covers on third of the pond on day 41 then the next day, on day 42, it will have tripled and now covers the whole pond.

2 marks

2.2 What fraction of the pond was the lily covering on day 39?

  • 181
  • 16
  • 19
  • 139
  • 127
  • (Not answered)

working backwards from day 42 where it covers the whole pond,

day 41 it covers 13 of the pond,

day 40 is covers 13 of 13 of the ponds, which is 19 of the pond,

on day 39 its covers 13 of 19 of the pond which is 127.

Before you hit the SUBMIT button, here are some quick reminders:

  • You will receive your score immediately, and collect your reward points.
  • You might earn a new badge... if not, then maybe next week.
  • Make sure you go through the solution sheet – it is massively important.
  • A score of less than 50% is ok – it means you can learn lots from your mistakes.
  • The next Parallelogram is next week, at 3pm on Thursday.
  • Finally, if you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelograms.

Cheerio, Simon and Ayliean.