# day/dydd 121 at 7puzzleblog.com T he Main Challenge

•  It is a 2-digit number,
•  It is an even number,
•  When the two digits are added together they make another 2-digit even number that is also a square number.

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

2   4   9   11   14   15   22   24   27   30   40   70   72   77

What is the difference between the sum of the multiples of 11 and the sum of the multiples of 10? 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 SIX ways of making 121 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 24 and 12 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

9    18    27    36    45    54    63    72    81    90

#9TimesTable

The Target Challenge

Can you arrive at 121 by inserting 4, 5, 6 and 7 into the gaps on each line?

•  (◯+◯)×(◯+◯) = 121
•  (◯+◯)²×(◯–◯) = 121
•  ◯³–◯×(◯–◯) = 121   