Answer
Alice had blackcurrant juice and scones.
Jane had orange juice and muffins.
Denise had strawberry juice and cake.
Frankie had blueberry juice and toast.
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Puzzle 206
Without using any reference material can you find the hidden countries? In each case, the letter indicates the first letter of the country in question, the number represents the number of letters in the country. For example, E7 would be England.
Z6, L10, I9, E7, B6, J7, P8, M10, P4, F4
Answer
Zambia, Luxembourg, Indonesia, Ecuador, Brazil (or Belize), Jamaica, Pakistan (or Paraguay), Mozambique (or Montenegro), Peru, Fiji.
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Puzzle 207
What four-digit number has Digit 1 three smaller than Digit 4, which is one more than Digit 2, which is twice Digit 3, which is one more than one third of Digit 4?
Answer
I asked for 9 foot 2 inches (110 inches) and my friend brought me 2 foot 9 inches (33 inches).
Reasoning
I asked my friend to buy me A feet and B inches, which is a total of 12A + B inches.
He accidentally bought me B feet and A inches, which is 12B + A inches.
We know that 12B + A is actually only 30% of what I wanted, so:
12B + A = 0.3 x (12A + B)
Multiply throughout by 10:
120B + 10A = 3 x (12A + B)
120B + 10A = 36A + 3B
117B = 26A
B = 26A ÷ 117
Don't forget that A and B can only be integers, and between 0 and 11.
Since 26 x A has to be at least 117, the lowest possible value for A is 5. We can check the remaining possibilities.
5 x 26 = 130
6 x 26 = 156
7 x 26 = 182
8 x 26 = 208
9 x 26 = 234 (*)
10 x 26 = 260
11 x 26 = 286
The only number wholly divisible by 117 is 234, which means that A = 9, and B = 2.
