# day/dydd 141 at 7puzzleblog.com

T he Main Challenge

One of our easier Mathelona-style challenges, still utilising the four arithmetic operations.  Place the eight digits 1 2 2 3 4 4 5 and 6 into the gaps so both lines work out:

◯  +  ◯   =    6    =   ◯  ×  ◯
◯  –  ◯   =    2    =   ◯  ÷  ◯

If you enjoy this type of number puzzle, click Mathelona for details of our pocket book of challenges.

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 & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

What is the difference between the two multiples of 7?

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

The Mathematically Possible Challenge

Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

4    8    12    16    20    24    28    32    36    40

#4TimesTable

The Target Challenge

Can you arrive at 141 by inserting 3, 5, 7 and 12 into the gaps on each line?

•  ◯×(◯+◯)–◯ = 141
•  (◯×◯+◯)×◯ = 141
•  ◯³+◯+◯–◯ = 141