# day/dydd 243 at 7puzzleblog.com

T he Main Challenge

We invite you to use seven 3’s (3 3 3 3 3 3 and 3) once each, with + – × ÷ available, to make various target numbers.

For instance, to make 1 and 2, you could do:

• 3 × (3÷3) – (3÷3) – (3÷3)  =  1
• (3+3) × (3÷3) × (3÷3) ÷ 3 =  2  . . .  and so on.

Continuing, as above, can you make the target numbers from 3 to 6?

The 7puzzle Challenge

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

The 5th & 7th rows of the playing board contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

Find three different numbers from the list that have a sum of 100.

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 THIRTEEN different ways to make 243 when using Lagrange’s Theorem. How many of them can you find?

The Mathematically Possible Challenge

Using 25 and 10 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

12    24    36    48    60    72    84    96    108    120

#12TimesTable

The Target Challenge

Can you arrive at 243 by inserting 2, 3, 4, 5 and 6 into the gaps below?

•  ◯×(◯+◯)²+(◯+◯)² = 243

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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