# day/dydd 249 at 7puzzleblog.com T he Main Challenge

Here’s a challenging number trail question involving seven arithmetical steps.  Start with the number 139, then:

8     +103     decrease by 50%     37     +109     1/3 of this     ÷7     =     ? 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 of the playing board contain the following fourteen numbers:

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

How many pairs of numbers have a sum of 75? 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 TEN different ways to make 249 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 58 and 11 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable The Target Challenge

Can you arrive at 249 by inserting 1, 2, 3, 4 and 5 into the gaps below?

•  (◯×◯÷◯)–√◯ = 249   