# day/dydd 197 at 7puzzleblog.com T he Main Challenge

There is just one set of three consecutive numbers in ascending order whose sum is less than 50 and follow this sequence:

•  prime number – cube number – square number

What is the sum of these three numbers? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 6th & 7th rows of the playing board contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

What is the sum of the multiples of 11? 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).

Show how you can make 197, in SEVEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

2    3    5    7    11    13    17    19    23    29 The Target Challenge

Can you arrive at 197 by inserting 1411 and 14 into the gaps on each line?

•  ◯×(◯+◯)–◯ = 197
•  (◯+◯)²–(◯×double◯) = 197   