Track / Stage 5 / 26 of 400 #626 of 2000

Problem 626

AIME late

Combinatorics Difficulty 5.1 Find the answer

3. (3 points) Define a new operation: $a \& b=(a+1) \div b$ , find the value of: $2 \&(3 \& 4)$

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Your answer

Official solution

3. (3 points) Define a new operation: $a \& b=(a+1) \div b$ , find: $2 \&(3 \& 4)$ , the value is $\qquad$ 3 .

【Solution】Solution: $2 \&(3 \& 4)$ ,
$\begin{array}{l} =(2+1) \div[(3+1) \div 4], \\ =3 \div 1, \\ =3 \end{array}$

Therefore, the answer is: 3 .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.