# day/dydd 181 at 7puzzleblog.com

T he Main Challenge

Your task is to arrive at the target numbers 66, 77, 88 and 99 by using the five numbers 1, 2, 3, 4 and 5 once, and with + – × ÷ available in each calculation.

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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

What is a quarter of the highest multiple of 10?

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 (or 4+1+1+1).

Show how you can make 181, in EIGHT different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which are the FIVE target numbers it is 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 181 by inserting 8, 9, 10 and 11 into the gaps on each line?

•  ◯×(◯+◯)+◯ = 181
•  ◯×(◯+◯)–◯ = 181

Answers can be found here.

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