DAY 166:

The Main Challenge

This number trail has seven arithmetical steps.  Start with the number 49, then:

√      add nineteen      50% of this      2      +26      subtract nine      ÷7      =      ?

What is your final answer?

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 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

What is the sum of the factors of 24?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 166, in NINE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which are the only THREE numbers it’s 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 166 by inserting 4, 7, 14 and 17 into the gaps on each line?

  •  (◯×◯)+(◯×◯) = 166
  •  (◯+◯)²+◯+double◯ = 166
  •  ◯×(◯+◯)–(◯+50%) = 166

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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