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3388
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Age 11 to 14 Challenge Level:
On the first day he decided to keep ${\bf \frac{3}{4}}$ of his peaches.
He gave the rest away. Then he ate one.
He gave the rest away. Then he ate one.
On the third day he decided to keep ${\bf \frac{5}{9}}$ of his peaches.
He gave the rest away. Then he ate one.
He gave the rest away. Then he ate one.
On the fifth day he decided to keep ${\bf \frac{2}{3}}$ of his peaches.
He gave the rest away. Then he ate one.
How many did he have left at the end?
(ii) A little monkey had 75 peaches.
Each day, he kept a fraction of his peaches, gave the rest away, and then ate one.
These are the fractions he decided to keep: $$ \frac{1}{2} \qquad \frac{1}{4} \qquad \frac{3}{4} \qquad \frac{3}{5} \qquad \frac{5}{6} \qquad \frac{11}{15}$$
In which order did he use the fractions so that he was left with just one peach at the end?
- Each fraction must be in its simplest form and must be less than 1.
- The denominator is never the same as the number of peaches left.
For example, if there were 45 peaches left, he would not choose to keep $\frac{44}{45}$ of them.
Click here for a poster of part (ii) of this problem.
NRICH is part of the family of activities in the Millennium Mathematics Project.