# day/dydd 78 at 7puzzleblog.com

T he Main Challenge

Using the three numbers 5, 5 and 5 once each, with + – × ÷ available, which SEVEN target numbers from 1-30 are mathematically possible to achieve?

The 7puzzle Challenge

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

The 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

Which four different numbers 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 FOUR ways of making 78 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 23 and 11 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable

The Target Challenge

Can you arrive at 78 by inserting 2, 4, 5 and 8 into the gaps on each line?

•  ◯×◯×◯–√◯ = 78
•  (◯+◯)×(◯+◯) = 78
•  (◯²–◯)×◯+ = 78