day/dydd 68 at 7puzzleblog.com

T he Main Challenge

Can you arrive at the target number 105 in two different ways when using the five numbers 1, 2, 3, 4 and 5 once in each calculation, and with + – ×  ÷ available?

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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

What is the difference between the highest multiple of 9 and highest multiple 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).

There are FOUR ways of making 68 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

5    10    15    20    25    30    35    40    45    50

#5TimesTable

The Target Challenge

Can you arrive at 68 by inserting 2, 3, 6 and 8 into the gaps on each line?

•  (◯+◯)×+ = 68
•  ◯²×(◯+◯+◯) = 68
•  (◯+◯)×–◯² = 68