# DAY/DYDD 64: The Main Challenge

From the numbers 1-30, eliminate the following:

• numbers containing the digit 1
• prime numbers
• numbers in the 20’s
• factors of 72

What is the only number that remains? 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 & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

What is the sum of the square numbers? 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 TWO ways of making 64 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

The Target Challenge

Can you arrive at 64 by inserting 4, 6, 8 and 10 into the gaps on each line?

•  (◯+◯)×(◯–◯) = 64
•  ◯×(◯+◯–◯) = 64
•  ◯²×(◯+◯)÷◯ = 64
•  ◯×(◯–◯)×√◯ = 64 Answers can be found here. Click Paul Godding for details of online maths tuition. This entry was posted in 7puzzleblog.com. Bookmark the permalink.

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