# day/dydd 146 at 7puzzleblog.com

T he Main Challenge

Apart from 987631 (9+8+7+6+3+1), can you find the other FOUR ways to make 34 when adding together six unique digits from 1-9?

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 2nd & 6th rows contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

What is the sum of the multiples of 6?

The Lagrange Challenge

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

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

Show how you can make 146, in NINE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the only THREE numbers it’s possible to make from the list below?

9    18    27    36    45    54    63    72    81    90

#9TimesTable

The Target Challenge

Can you arrive at 146 by inserting 8, 9, 11 and 14 into the gaps on each line?

•  (◯+◯)×◯–◯ = 146
•  ◯²+◯+◯+√◯ = 146

Answers can be found here.

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