# day/dydd 142 at 7puzzleblog.com

T he Main Challenge

From the numbers 1-20, eliminate all:

• square numbers
• prime numbers
• triangular numbers
• multiples of 6

Add together the numbers that remain; what is your total?

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 1st & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

From this list, what is the sum of the multiples of 8?

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 FIVE ways of making 142 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

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

5    10    15    20    25    30    35    40    45    50

#5TimesTable

The Target Challenge

Can you arrive at 142 by inserting 4, 9, 10 and 13 into the gaps on each line?

•  ◯×◯+◯×◯ = 142
•  ◯×◯+◯×√◯ = 142

Answers can be found here.

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