An envelope has space for at most 3 stamps. I | vedclass

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(A) An envelope can hold at most $3$ stamps. We have three stamps of value $1$ and three stamps of value $a$.Possible values formed by $n$ stamps $(n

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(A) An envelope can hold at most $3$ stamps. We have three stamps of value $1$ and three stamps of value $a$.Possible values formed by $n$ stamps $(n \le 3)$ are:$1$ stamp: $1, a$$2$ stamps: $1+1=2, 1+a, a+a=2a$$3$ stamps: $1+1+1=3, 1+1+a=a+2, 1+a+a=2a+1, a+a+a=3a$If $a=2$,the possible values are: $1, 2, 3, 4, 5, 6$.The smallest positive integer that cannot be formed is $7$.If $a > 2$,say $a=3$,the values are: $1, 3, 2, 4, 6, 3, 5, 7, 9$. The smallest missing value is $4$.Since the question implies a unique answer independent of $a$ for a specific condition,and $a=2$ is the smallest integer $a > 1$,the least positive integer that cannot be formed is $7$.

An envelope has space for at most $3$ stamps. If you are given three stamps of denomination $1$ and three stamps of denomination $a$ (where $a > 1$),what is the least positive integer for which there is no possible stamp value?

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