# day/dydd 174 at 7puzzleblog.com

T he Main Challenge

Read the facts below:

• I am a 2-digit number,
• I am a multiple of 7,
• The difference between my two digits is 4.

Which number am I?

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

Which number, when 1 is subtracted from it, becomes a square number?

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 174, in NINE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

1    3    6    10    15    21    28    36    45    55    66

#TriangularNumbers

The Target Challenge

Can you arrive at 174 by inserting 9, 10, 16 and 20 into the gaps on each line?

•  (◯+◯)×(◯–◯) = 174
•  ◯×◯+◯–◯ = 174

Answers can be found here.

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