day/dydd 123 at 7puzzleblog.com

T he Main Challenge

From the numbers 1-30 inclusive, delete:

• multiples of 5
• factors of 36
• numbers containing a ‘7’
• prime numbers
• even numbers

Which is the only number that remains?

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

Which three different numbers on the list have a sum of 100?

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 123 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?

12    24    36    48    60    72    84    96    108    120

#12TimesTable

The Target Challenge

Can you arrive at 123 by inserting 3, 9, 10 and 12 into the gaps on each line?

•  ◯×◯+◯÷◯ = 123
•  ◯×◯+half(◯×◯) = 123
•  (◯+◯)×◯+half◯ = 123