DAY 220:

The Main Challenge

The ten letters, A-J, in the following two sections each contains a calculation. Which is the only letter that has the same answer in both sections?

E:6÷6 I:5+1 G:3+2 A:10–2 J:4+3 C:5×1 F:6÷3 B:8–4 H:9÷3 D:4×2

H:4–3 A:6÷1 I:3×3 B:6–1 F:6–4 J:8÷2 E:5×2 G:4×1 D:9–3 C:2+1

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 3rd & 4th rows of the playing board contain the following fourteen numbers:

3 10 13 25 32 35 36 42 44 45 54 60 66 80

What is the difference between the two largest odd numbers?

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 NINE different ways to make 220 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 4, 6 and 9 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

1 4 9 16 25 36 49 64 81 100

#SquareNumbers

The Target Challenge

Can you arrive at 220 by inserting 5, 10, 20 and 30 into the gaps on each line?

Answers can be found here.

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