Читать книгу The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind - Литагент HarperCollins USD, F. M. L. Thompson - Страница 26

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Week 13

85. The Beans’ beans

The Bean family are very particular about beans. At every meal all Beans eat some beans. Pa Bean always eats more beans than Ma Bean but never eats more than half the beans. Ma Bean always eats the same number of beans as both of their children together and the two children always eat the same number of beans as each other. At their last meal they ate 23 beans.

How many beans did Pa Bean eat?

[SOLUTION]

86. Palindromic years

The number 2002 is a palindrome, since it reads the same forwards and backwards.

For how many other years this century will the number of the year be a palindrome?

[SOLUTION]

87. Swallowing spiders

It was reported recently that, in an average lifetime of 70 years, each human is likely to swallow around 8 spiders while sleeping.

Supposing that the population of the UK is around 60 million, what is the best estimate of the number of unfortunate spiders consumed in this way in the UK each year?

[SOLUTION]

88. Multiple missing digits

The two-digit by two-digit multiplication shown has lots of digits missing.


What are the missing digits?

[SOLUTION]

89. Pippa’s visit

Pippa is visiting her grandparents. She spends half the time playing, a third sleeping and the remaining 35 minutes eating.

How long is her visit?

[SOLUTION]

90. Possible ps

The eight-digit number ‘ppppqqqq’, where p and q are digits, is a multiple of 45.

What are the possible values of p?

[SOLUTION]

91. A magic square

A 3 × 3 grid contains nine numbers, not necessarily integers, one in each cell. Each number is doubled to obtain the number on its immediate right and trebled to obtain the number immediately below it.


The sum of the nine numbers is 13. What is the number in the central cell?

[SOLUTION]

The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind

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