# day/dydd 122 at 7puzzleblog.com

T he Main Challenge

Find the sum of the first SEVEN whole numbers that has a 3 or 5 as part of their number OR are multiples of 3 or 5.

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 highest and lowest 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 EIGHT ways of making 122 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

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

10    20    30    40    50    60    70    80    90    100

#10TimesTable

The Target Challenge

Can you arrive at 122 by inserting 2, 4, 7 and 10 into the gaps on each line?

•  ◯²+◯×(◯+◯) = 122
•  (◯+◯)²–double(◯+◯) = 122
•  ◯⁴÷◯+double(◯–◯) = 122