[pudley4]

Work it backwards:

At the end, G=40, T=40, H=40

If Gary gave Tom and Hal enough tickets to double their holdings, then before this transaction, T=40/2=20, H=40/2=20, G=40+20+20=80

If Tom gave tickets to Hal and Gary, then before he did, H=10, G=40, T=70

If Hal gave tickets to Gary and Tom, then before he did, G=20, T=35, H=65