# day/dydd 124 at 7puzzleblog.com

T he Main Challenge

A palindromic number is a number that can be read the same forwards and backwards (e.g. 333 and 797).  How many palindromic numbers are there between 100 and 1,000?

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 sum of the multiples of 9?

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

The Mathematically Possible Challenge

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

1    4    9    16    25    36    49    64    81    100

#SquareNumbers

The Target Challenge

Can you arrive at 124 by inserting 5, 8, 10 and 16 into the gaps on each line?

•  (◯+◯)×◯+√◯ = 124
•  ◯×◯–(◯÷◯)² = 124
•  (◯–◯÷◯)×◯ = 124