# day/dydd 193 at 7puzzleblog.com

T he Main Challenge

When playing Mathematically Possible, players must analyse which numbers can (or can’t) be made from the three numbers rolled on their dice.

Using the numbers 3, 4 and 6, with + – × ÷ available, which THREE of the following target numbers are NOT mathematically possible to achieve?

1   2   3   5   6   7   8   10   12   13   14   18   21   22   24   27   30

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 4th & 5th rows of the playing board contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

What is the difference between the sum of the multiples of 5 and sum of the multiples of 6?

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).

Show how you can make 193, in EIGHT different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which SIX numbers is it 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 193 by inserting 7, 10, 11 and 13 into the gaps on each line?

•  ◯×(◯+◯)+◯ = 193
•  ◯²+◯²+◯+◯ = 193

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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