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Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

What Two ...?

Age 7 to 11 Short
Challenge Level

Louise of Headington Junior School gives the answer of 237 and 238.

"I worked this out by finding the square root of 56,406 and then wrote down the whole number (237) and rounded it up to 238".

Class 7P from Loretto Junior, Musselburgh apporached this problem using trial and improvement which is a very useful strategy:

Kitty said let's try 600 x 600 = 360000 and that is too big!
Angus said let's try 100 x 100 = 10000 and that is too small.
Ashleigh thought 200 x 200 was 40000 which was a little too small.
Graeme knew that 250 x 250 was 62,500 - close!
Sophie offered 230 x 230 which is 52,900 - getting there.
Gair now tried 240 x 240 and got 57,600.
Tom provided the masterstroke and said our number 56406 should be in the high 230s , so we looked at 236x 237 but the last digit is a 2 because 6x7 = 42.
Finally Caitlin shouted in excitement 'try 237x 238 as the last digit will be a 6'. The answer therefore is 237 x 238.