day/dydd 52 at 7puzzleblog.com

T he Main Challenge

Find the sum of the FIVE 2-digit numbers that are even, has digits adding up to more than 10 and are not multiples of 3, 4 or 7.

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 1st & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

What is the sum of the factors of 36 listed above?

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 52 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

60    61    62    63    64    65    66    67    68    69

#NumbersIn60s

The Target Challenge

Can you arrive at 52 by inserting 4, 6, 8 and 9 into the gaps on each line?

•  ◯×◯–◯÷◯ = 52
•  ◯²–(◯+√◯×√◯) = 52
•  ◯²+◯×(◯–◯)² = 52
•  (√◯×◯+◯)×√ = 52