# day/dydd 95 at 7puzzleblog.com

T he Main Challenge

Can you place the numbers 0 1 1 2 2 3 3 4 6 6 7 and 7 into the 12 gaps below so that all three lines work out arithmetically?

◯  +  ◯   =    2    =   ◯  –  ◯
◯  +  ◯   =    9    =   ◯  ×  ◯
◯  +  ◯   =    7    =   ◯  ÷  ◯

Click Mathelona for details of the above number puzzle if you want to try more!

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 6th & 7th rows contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

What is the sum of the factors of 60 in this list?

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 THREE ways of making 95 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 57 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

8    16    24    32    40    48    56    64    72    80

#8TimesTable

The Target Challenge

Can you arrive at 95 by inserting 2, 3, 4 and 5 into the gaps on each line?

•  (◯³+²+◯)×◯ = 95
•  ◯²×–(◯+◯) = 95
•  +◯×(◯+◯) = 95

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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