Cheapest way to build or buy a remote controlled sound maker?
simulate this circuit &ndash; Schematic created using CircuitLab

Assuming you buy about 25 of each:

An Attiny is about $1. A small speaker is about $2. A MOSFET to drive it is about $0.25. A small 3.7V LiPo battery is about $2. The Atmega can run on the built-in ceramic resonator at 1 MHz or 8 MHz when fed 3V or better. 1 MHz (and perhaps sleep mode) will extend the lifetime, although you'll likely get a couple of days of battery life even without that.

http://www.digikey.com/product-detail/en/ATTINY85-20PU/ATTINY85-20PU-ND/735469
http://www.digikey.com/product-detail/en/2403%20260%2000031/423-1172-1-ND/3854653
http://www.digikey.com/product-detail/en/BS170/BS170-ND/244280
http://www.hobbypartz.com/250mah.html

The Attiny can be programmed to wait for a random amount of time, and then make a noise on the output pin that drives the MOSFET/speaker. You'll need a USB programmer and a socket to program the chips in, which adds about $10 of one-time cost.

http://www.amazon.com/SainSmart-Programmer-ATMEL-ATMega-ATTiny/dp/B0051SRZWC

plus a breadboard and some jumper wires for programming.