The CDC 1604, released in 1960, was Seymour Cray's first supercomputer, and also one of the first computers made of transistors. (The IBM 7090 was released only the previous year.)
How many transistors went into the CDC 1604?
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The information to answer the question "exactly" is available on the internet, but I'm not going to do the arithmetic for you!
The Maintenance Manual (http://bitsavers.org/pdf/cdc/1604/033a_1604_Computer_Vol_3_Maintenance_Dec60.pdf) Appendix B gives the schematic of each printed circuit card, so you can count the number of transistors on each.
The last page of the Customer Engineering Instruction Manual (http://bitsavers.org/pdf/cdc/1604/60118700A_CDC_1604A_Customer_Engineering_Instruction_Manual_Sep1966.pdf) gives the number of each type of card in the complete computer.
My "quick eyeball" estimate would be about 6,000 printed circuit cards with a total of 25,000 transistors.
That is comparable with this Wikipedia page https://en.wikipedia.org/wiki/Transistor_count#Transistor_computers which gives 30,000 transistors + 22,000 diodes for the IBM 7070, and 50,000 transistors for the IBM 7090.