day/dydd 66 at 7puzzleblog.com

T he Main Challenge

When multiplying two numbers together and then adding or subtracting a third number, there are four ways of reaching 60 when the three numbers used in each calculation are in the range 1-9, and can be repeated.

One way to make 60 is (9×6)+6; can you find the other three?

[Note:  (9×6)+6 and (6×9)+6 counts as just one way.]

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

How many pairs of consecutive numbers are there?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are SIX ways of making 66 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable

The Target Challenge

Can you arrive at 66 by inserting 2, 3, 4 and 9 into the gaps on each line?

•  (◯×◯+◯)× = 66
•  (◯×◯–◯)× = 66
•  ◯²×◯+◯× = 66
•  ◯³+(◯+◯)²+√◯ = 66

Answers can be found here.

Click Paul Godding for details of online maths tuition.

This entry was posted in 7puzzleblog.com. Bookmark the permalink.

This site uses Akismet to reduce spam. Learn how your comment data is processed.